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Questions and Answers

What is a vector in MATLAB?

  • A collection of strings
  • A two-dimensional array of numbers
  • An array with only non-zero elements
  • A one-dimensional array of numbers (correct)

How can a column vector be created in MATLAB?

  • By defining the vector as a function of another vector
  • By enclosing numbers in rectangular brackets and separating them by commas
  • By using the transpose operator on a row vector
  • By enclosing a set of semicolon delimited numbers in square brackets (correct)

What does scalar multiplication of a vector entail?

  • Subtracting a scalar from each component of the vector
  • Multiplying each component of the vector by a scalar value (correct)
  • Adding a vector to itself a number of times
  • Creating a new vector with fewer components

Which of the following correctly creates a row vector in MATLAB?

<p>Both B and C (A)</p> Signup and view all the answers

What is the outcome of transposing a column vector?

<p>It becomes a row vector with the same elements (B)</p> Signup and view all the answers

Which MATLAB command would yield 'b' as defined in the content?

<p>b = 3 * a; (D)</p> Signup and view all the answers

What does the MATLAB transpose operator look like?

<p>It is represented by a single quote (’) (B)</p> Signup and view all the answers

What is the primary reason MATLAB is useful for linear algebra?

<p>It has exceptional capabilities for handling arrays of numbers (D)</p> Signup and view all the answers

What MATLAB command would you use to convert Fahrenheit temperatures stored in an array called temps to Celsius?

<p>CelsiusTemps = (5/9) * (temps - 32) (D)</p> Signup and view all the answers

Which of the following is a correct way to end a MATLAB session?

<p>Type 'quit' in the command window (B)</p> Signup and view all the answers

If the variable y has not been assigned a value, which of the following operations will MATLAB allow?

<p>x = y ^ 2 (C)</p> Signup and view all the answers

What will MATLAB return when you define the temperatures in the temps array as temps = [32, 50, 65, 70, 85] and then enter 'TemperatureData' in the command window?

<p>The list of temperatures in the array (D)</p> Signup and view all the answers

How is the volume of a cylinder calculated in MATLAB if the height is h and the radius is r?

<p>V = π * r^2 * h (A)</p> Signup and view all the answers

What result will MATLAB return when you compute the sine of $\frac{\pi}{3}$?

<p>$\frac{\sqrt{3}}{2}$ (B)</p> Signup and view all the answers

What is the correct way to store and access an array of data in MATLAB?

<p>Write it and save it in an M-file for later use (B)</p> Signup and view all the answers

When you create an M-file called TemperatureData.m, how should you access the data within it in MATLAB?

<p>Simply type TemperatureData (D)</p> Signup and view all the answers

What is the determinant of the coefficient matrix A in the given system of equations?

<p>6 (D)</p> Signup and view all the answers

If a system of equations has more unknowns than equations, how is the system classified?

<p>Underdetermined (C)</p> Signup and view all the answers

What happens to the number of solutions when the determinant of the coefficient matrix A equals 0?

<p>There are infinite solutions. (D)</p> Signup and view all the answers

In the example system, if y can assume any value, how can x and z be expressed in terms of y?

<p>x = 3 - 7y; z = -5y (A)</p> Signup and view all the answers

Which of the following statements about a square coefficient matrix is true for finding an inverse?

<p>The matrix must be non-singular. (B)</p> Signup and view all the answers

What is the role of the pseudoinverse in systems of equations?

<p>To provide the minimum norm solution when the determinant is zero. (B)</p> Signup and view all the answers

After finding x = inv(A) * b, what are the resulting values of x?

<p>-1 and -4 (C)</p> Signup and view all the answers

What does an underdetermined system imply regarding variable determination?

<p>Some variables are free to take any value. (A)</p> Signup and view all the answers

What does the syntax x = [xi : q : xe] accomplish in MATLAB?

<p>It generates a vector with uniformly spaced elements. (A)</p> Signup and view all the answers

What will be the output of the command x = [0:0.1:1]?

<p>A list of floating-point numbers from 0 to 1 with a step of 0.1. (D)</p> Signup and view all the answers

What command is used in MATLAB to add a grid to a plot?

<p>grid on (D)</p> Signup and view all the answers

Which command would result in a matrix error in MATLAB?

<p>y = x^2 (C)</p> Signup and view all the answers

What does the 'axis square' command do in MATLAB?

<p>Makes the plot square-shaped (B)</p> Signup and view all the answers

How do you create a decrementing vector from 100 to 80 with an increment of -5?

<p>u = [100:-5:80] (A)</p> Signup and view all the answers

If you want the axis limits in MATLAB to be set automatically, which command should you use?

<p>axis auto (A)</p> Signup and view all the answers

What does the command linspace(a,b) do?

<p>It generates 100 regularly spaced elements between a and b. (C)</p> Signup and view all the answers

What is the purpose of the 'axis equal' command in MATLAB?

<p>To maintain equal proportions between length and width (D)</p> Signup and view all the answers

If you want to create a vector containing values between 0 and 10 with a spacing of 2, which command is correct?

<p>x = [0:2:10] (A)</p> Signup and view all the answers

When plotting using 'plot(x, y), grid on, axis equal', what aspect of the plot will be notably different from using only 'plot(x, y), grid on'?

<p>The spacing on the axes (D)</p> Signup and view all the answers

What is the result of y = x^2 when x is a vector?

<p>It returns an error because x is not a square matrix. (C)</p> Signup and view all the answers

Which of the following functions was used to create the y-values in the example given?

<p>y = exp(-1.2*x).<em>sin(10</em>x + 5) (B)</p> Signup and view all the answers

How do you create a row vector of n regularly spaced elements between a and b in MATLAB?

<p>Using the command linspace(a,b,n). (A)</p> Signup and view all the answers

What does the command 'plot(x,y)' accomplish in MATLAB?

<p>Generates a two-dimensional plot of y against x (A)</p> Signup and view all the answers

Which command can be used to explore different styles of plots in MATLAB?

<p>axis command (B)</p> Signup and view all the answers

What is the primary purpose of using the fplot function in MATLAB?

<p>To automatically determine the number of plotting points (B)</p> Signup and view all the answers

What error occurs when using 'exp(-t)*sin(t)' in MATLAB?

<p>Inner matrix dimensions must agree (A)</p> Signup and view all the answers

Which command adds titles and labels to a plot generated by fplot?

<p>title('Damped Spring Forcing'), xlabel('t'), ylabel('f(t)') (C)</p> Signup and view all the answers

When defining a function to avoid errors in MATLAB, what character is necessary before the multiplication symbol?

<p>. (D)</p> Signup and view all the answers

What should the correct syntax be to define the function f for plotting using the exponential and sine functions?

<p>f = exp(-2<em>t) .</em> sin(t); (D)</p> Signup and view all the answers

How is the plot function called to visualize the function f between 0 and 4?

<p>plot([0:0.01:4], f) (D)</p> Signup and view all the answers

What does the argument 'function string' in the fplot function specify?

<p>The mathematical expression to plot (A)</p> Signup and view all the answers

If we wanted to plot the function f(t) = e^{-2t}sin(t), which of the following would be the correct fplot command to use?

<p>fplot('exp(-2*t)*sin(t)', [0, 4]) (C)</p> Signup and view all the answers

Flashcards

MATLAB Output

MATLAB displays results in the command window. It can show numbers, vectors, or the result of calculations.

M-files

Text files in MATLAB used to store commands that can be run later.

MATLAB variables

Named locations in MATLAB memory to hold values. Examples include temps and CelsiusTemps.

Ending a MATLAB session

Closing the MATLAB program. Can be done through a menu or typing quit in the command window.

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MATLAB calculation

MATLAB can compute mathematical expressions and operations.

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Storing data in MATLAB

Data can be stored in M-files or assigned to variables in memory.

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MATLAB function

A self-contained block of MATLAB code that performs a specific task.

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Cylinder Volume

The volume of a cylinder is calculated using the formula: V=Ï€r^2h.

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Column Vector

A one-dimensional array of numbers arranged vertically in MATLAB. Elements are separated by semicolons within square brackets.

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Row Vector

A one-dimensional array of numbers arranged horizontally in MATLAB. Elements are separated by spaces or commas within square brackets.

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Scalar Multiplication

Multiplying each element of a vector by a single number (scalar).

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Transpose of a vector

Changing a vector from a column to a row or vice-versa, represented by a single quote (').

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MATLAB

A software environment for numerical computation, particularly useful for linear algebra, due to its array handling capabilities.

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Vector Element

A single number in a vector.

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Vector Creation

Creating a vector in MATLAB using square brackets with elements separated by semicolons (column vector) or spaces/commas (row vector).

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Scalar Variable

A single numerical value used in mathematical operations within MATLAB.

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Creating vectors with uniform spacing

Vectors with equally-spaced elements between a starting and ending value are created using the syntax: [start_value : increment : end_value].

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Vector increment

The value by which elements in a vector are separated. Specified after the starting value.

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[start_value: increment : end_value]

Syntax used to create a vector with regularly-spaced elements in MATLAB.

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linspace command

Creates a vector with n equally-spaced elements between a and b. linspace(a,b,n)

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Row vector generation

Creates a horizontal array or sequence of numbers.

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Negative increment

The increment value can be negative to create elements decreasing in value.

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Uniformly spaced elements

Elements in a vector that are separated by a fixed interval.

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Creating x values for plotting

Using uniform spacing in a vector can be used to create points which can be plotted.

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Inverse Matrix

A matrix that, when multiplied by the original matrix, results in an identity matrix.

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Determinant

A value calculated from a square matrix; tells us if an inverse exists.

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System of Equations

A set of equations involving multiple unknowns to be solved simultaneously.

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Underdetermined System

System with fewer equations than unknowns, having infinitely many solutions.

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Pseudoinverse

A generalized inverse used to find a solution when the original inverse doesn't exist (e.g., for underdetermined systems).

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Coefficient Matrix

A matrix representing the coefficients of the variables in a system of equations.

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Linear System

A system of equations where each equation is linear in the variables.

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Infinite Solutions

A system of equations that has more than one solution.

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MATLAB Plotting Error

Error in MATLAB when multiplying functions in an expression, like exp(-t)*sin(t), because the dimensions of the functions don't match.

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fplot function

MATLAB function that plots a function without needing to specify the number of plotting data points, avoids errors related to matrix multiplication when plotting mathematical expressions.

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Function String

Text representation of a function to be plotted in fplot function.

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fplot Command Syntax

Method for plotting with fplot: fplot('function string', [xstart, xend]) where function string specifies the function to plot and xstart, xend give the interval.

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. Multiplication Symbol

MATLAB notation to perform element-wise multiplication. Essential for multiplying functions in expressions.

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Vector Element-wise Multiplication

Performing multiplication between corresponding elements in MATLAB vectors.

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Matrix Dimensions

The size and arrangement of the elements in a matrix (rows and columns) in MATLAB; the dimensions must align for matrix multiplication operations to succeed.

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MATLAB Plotting

MATLAB command to create graphical visualizations of data or defined functions.

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Plot with grid

Adds a grid to the plot, making it easier to read data.

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Axis square

Makes the plot dimensions square, ensuring equal scaling on both axes.

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Axis equal

Adjusts plot axes to have the same scaling and tick spacing.

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Axis auto

Lets MATLAB automatically determine axis limits.

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Creating x values

Generating a sequence of x values for plotting a function.

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Plot commands

MATLAB commands used to create plots, such as plot(x,y).

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Matrix multiplication

Using the .* operator to perform element-wise multiplication.

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Uniformly spaced vector

Vector where elements are equally-spaced; useful for plotting.

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