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Questions and Answers
What are the dimensions of matrix A given in the example?
What are the dimensions of matrix A given in the example?
- 2 × 2
- 2 × 3
- 3 × 2
- 3 × 3 (correct)
Which entry corresponds to a31 in matrix A?
Which entry corresponds to a31 in matrix A?
- 7
- 3 (correct)
- 2
- 0
Which of the following correctly defines a row matrix?
Which of the following correctly defines a row matrix?
- A matrix with equal rows and columns
- A matrix with more rows than columns
- A matrix with dimensions 1 × n (correct)
- A matrix with dimensions m × 1
What must be true for matrices to be added or subtracted?
What must be true for matrices to be added or subtracted?
What is the name given to a matrix with the same number of rows and columns?
What is the name given to a matrix with the same number of rows and columns?
If matrix A has dimensions 3 × 3, how many entries does it have?
If matrix A has dimensions 3 × 3, how many entries does it have?
To locate the entry a22 in matrix A, you should look for which row and column?
To locate the entry a22 in matrix A, you should look for which row and column?
What characterizes a column matrix?
What characterizes a column matrix?
What is a requirement for two matrices to be added together?
What is a requirement for two matrices to be added together?
What happens if you try to add a 2 × 3 matrix to a 3 × 3 matrix?
What happens if you try to add a 2 × 3 matrix to a 3 × 3 matrix?
If matrix A is 3 × 4 and matrix B is 4 × 2, what is the dimension of the product matrix AB?
If matrix A is 3 × 4 and matrix B is 4 × 2, what is the dimension of the product matrix AB?
What would happen if you attempted to multiply a 3 × 4 matrix by a 2 × 5 matrix?
What would happen if you attempted to multiply a 3 × 4 matrix by a 2 × 5 matrix?
If A = [[3, 4], [2, 5]] and you multiply A by the scalar 2, what is the resulting matrix?
If A = [[3, 4], [2, 5]] and you multiply A by the scalar 2, what is the resulting matrix?
Which of the following statements about matrix multiplication is true?
Which of the following statements about matrix multiplication is true?
Given matrices A (3 × 2) and B (2 × 3), what can you say about the product BA?
Given matrices A (3 × 2) and B (2 × 3), what can you say about the product BA?
In scalar multiplication, which statement is incorrect?
In scalar multiplication, which statement is incorrect?
What is the result of the matrix multiplication A*B?
What is the result of the matrix multiplication A*B?
Which function would be best used to create a 5-by-1 column vector of zeros in MATLAB?
Which function would be best used to create a 5-by-1 column vector of zeros in MATLAB?
Which operation would not produce the expected output in matrix operations?
Which operation would not produce the expected output in matrix operations?
What does the intensity of an image refer to at a point (x, y)?
What does the intensity of an image refer to at a point (x, y)?
Which MATLAB function is used to find the determinant of a matrix?
Which MATLAB function is used to find the determinant of a matrix?
In matrix A=[1 2; 3 4; 5 6], what is the value at the second row and first column?
In matrix A=[1 2; 3 4; 5 6], what is the value at the second row and first column?
What results from using the rand function in MATLAB?
What results from using the rand function in MATLAB?
What would be the correct MATLAB command to transpose a matrix?
What would be the correct MATLAB command to transpose a matrix?
What is the result of adding 10 to each entry of the matrix A = [1 2; 3 4]?
What is the result of adding 10 to each entry of the matrix A = [1 2; 3 4]?
What operator is used to transpose a matrix?
What operator is used to transpose a matrix?
What happens when you attempt to calculate the inverse of a singular matrix?
What happens when you attempt to calculate the inverse of a singular matrix?
When using the .* operator on the matrix A = [1 2; 3 4], what is the result of P = A .* A?
When using the .* operator on the matrix A = [1 2; 3 4], what is the result of P = A .* A?
Which of the following describes the result of A.^3 for A = [1 2; 3 4]?
Which of the following describes the result of A.^3 for A = [1 2; 3 4]?
What is the primary difference between A * B and A .* B?
What is the primary difference between A * B and A .* B?
What is the consequence of trying to calculate P = A * inv(A) for a singular matrix A?
What is the consequence of trying to calculate P = A * inv(A) for a singular matrix A?
What is concatenation in the context of matrix operations?
What is concatenation in the context of matrix operations?
What method is used to concatenate arrays next to one another?
What method is used to concatenate arrays next to one another?
Which command would you use to rotate a matrix by 90 degrees?
Which command would you use to rotate a matrix by 90 degrees?
In matrix indexing, what does A(4,2) return if A is defined as A = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]?
In matrix indexing, what does A(4,2) return if A is defined as A = [16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]?
What happens if you attempt to assign a value to an array index that is outside its current dimensions?
What happens if you attempt to assign a value to an array index that is outside its current dimensions?
What does the colon operator do in matrix operations?
What does the colon operator do in matrix operations?
In concatenating two arrays A and B along a specified dimension, which argument must be provided to the function 'cat'?
In concatenating two arrays A and B along a specified dimension, which argument must be provided to the function 'cat'?
Which of the following is true about accessing elements using the single subscript method?
Which of the following is true about accessing elements using the single subscript method?
Which of the following best describes horizontal concatenation?
Which of the following best describes horizontal concatenation?
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Study Notes
Describing Matrices
- A matrix is a rectangular array of numbers represented by a capital letter.
- Matrix entries (𝑎𝑖𝑗) are defined by their row (𝑖) and column (𝑗).
- Matrices are described by their dimensions: 𝑚 × 𝑛 (𝑚 rows, 𝑛 columns)
- A square matrix has the same number of rows and columns.
- A row matrix has one row (1 × 𝑛).
- A column matrix has one column (𝑚 × 1).
Matrix Operations
- Addition and Subtraction: Matrices can only be added/subtracted if they have the same dimensions. Corresponding entries are added/subtracted.
- Scalar Multiplication: Multiplying a matrix by a scalar involves multiplying each entry by the scalar.
- Matrix Multiplication:
- Possible only when the number of columns in the first matrix equals the number of rows in the second matrix (inner dimensions match).
- The resulting matrix's dimensions are determined by the outer dimensions.
- The product of two matrices is calculated by taking the dot product of rows from the first matrix with columns from the second matrix.
- MATLAB Commands:
- Transpose:
A'- Determinant:det(A)- Inverse:inv(A)
Matrices in MATLAB
-
Creating Matrices:
- Row vectors: Elements separated by commas or spaces (e.g.,
A=[1 2 3 4]) - Multiple rows: Rows separated by semicolons (e.g.,
A=[1 2 ;3 4;5 6]) - Functions:
ones(),zeros(),rand(),eye()
- Row vectors: Elements separated by commas or spaces (e.g.,
-
Matrix Operations:
- Adding a constant:
A+10 - Transposing:
A' - Matrix multiplication:
A*B - Element-wise multiplication:
A.*B - Element-wise power:
A.^3 - Concatenation:
- Horizontal:
[A A] - Vertical:
[A; A] - Specific dimension:
cat(dim, A, B)
- Horizontal:
- Rotation:
rot90(A)
- Adding a constant:
-
Matrix Indexing:
- Accessing elements:
- Row/column subscripts:
A(4,2) - Single subscript:
A(8)
- Row/column subscripts:
- Expanding matrix size:
A(4,5)=17 - Range of elements: Use the colon (
:), e.g.,A(1:2, 3:4)
- Accessing elements:
Image Representation in MATLAB
- Digital Images as Matrices:
- An image is represented by a 2D function 𝑓 (𝑥, 𝑦) where 𝑥 and 𝑦 are spatial coordinates.
- 𝑓 (𝑥, 𝑦) represents the intensity of the image at a specific point.
- A digital image is a MATLAB matrix with each element representing a pixel.
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