Recent

  • Show all results for ""
TAMU MATH 140 Matrix Operations Flashcards
26 Questions
101 Views

TAMU MATH 140 Matrix Operations Flashcards

Created by
@LowCostHarpy

Questions and Answers

What must matrices have for addition or subtraction?

  • Same number of columns
  • Different sizes
  • Same number of rows
  • Same size (correct)

    • What does matrix multiplication require?

    Inner values must be equal, to give a matrix of the outer values

    The commutative property states that for all mxn matrices, A+B = B+A.

    True

    What is the associative property of addition?

    <p>(a+b)+c=a+(b+c)</p> Signup and view all the answers

    What does the transpose of a matrix do?

    <p>MxN -&gt; NxM</p> Signup and view all the answers

    Which of the following is true about properties of matrix transposition?

    <p>(A+B)^T = A^T + B</p> Signup and view all the answers

    What defines matrix equality?

    <p>Only equal if they are the same size and corresponding entries are equal</p> Signup and view all the answers

    What is one of the properties of matrix multiplication?

    <p>All of the above</p> Signup and view all the answers

    What is the equation of a horizontal line?

    <p>y = b</p> Signup and view all the answers

    What is the equation of a vertical line?

    <p>x = a</p> Signup and view all the answers

    What is the point slope form of a line?

    <p>y - y1 = m(x - x1)</p> Signup and view all the answers

    What is the slope-intercept form of a line?

    <p>y = mx + b</p> Signup and view all the answers

    What is the standard form of a linear equation?

    <p>Ax + By = C</p> Signup and view all the answers

    What does the linear depreciation formula represent?

    <p>V(t) = mt + b</p> Signup and view all the answers

    What is the total cost formula?

    <p>C(x) = (production cost per item)(quantity) + (fixed cost) = mx + F</p> Signup and view all the answers

    What does revenue R(x) equal?

    <p>R(x) = (price per item)(quantity) = px</p> Signup and view all the answers

    How is profit P(x) calculated?

    <p>P(x) = R(x) - C(x)</p> Signup and view all the answers

    What does demand D(x) represent?

    <p>D(x) = price/p(x) = mx + b, always has a negative slope</p> Signup and view all the answers

    What does supply S(x) represent?

    <p>S(x) = price/p(x) = mx + b, always has a positive slope</p> Signup and view all the answers

    What defines an independent system?

    <p>A system of equations that has exactly one solution. M1 not equal to M2.</p> Signup and view all the answers

    What is an inconsistent system?

    <p>A system of equations that has no solution. M1 = M2 and B1 is not equal to B2.</p> Signup and view all the answers

    What is a dependent system?

    <p>A system of equations that has infinitely many solutions. M1 = M2 and B1 = B2.</p> Signup and view all the answers

    What is the break-even point?

    <p>Where R(x) = C(x), ordered pair: (BE quantity, BE revenue)</p> Signup and view all the answers

    What is the equilibrium point?

    <p>Where S(x) = D(x), ordered pair: (EQ quantity, EQ price)</p> Signup and view all the answers

    What is the reduced row echelon form (RREF)?

    <p>Each leading 1 is to the right of all leading 1s in the rows above</p> Signup and view all the answers

    What is pivoting?

    <p>Process of obtaining a 1 in a location and making all other entries zeros in that column</p> Signup and view all the answers

    Study Notes

    Matrix Operations

    • Matrix Addition/Subtraction: Only matrices of the same size can be added or subtracted.
    • Matrix Multiplication: Requires that inner dimensions are equal; resulting matrix dimensions are defined by the outer dimensions.
    • Commutative Property: For matrices A and B, A + B = B + A holds true.
    • Associative Property: The equation (a + b) + c = a + (b + c) applies to matrix addition.

    Matrix Transposition

    • Transpose of a Matrix: Transforming a matrix of size MxN to NxM.
    • Properties of Matrix Transposition:
      • If A is MxN, then A^T is NxM.
      • Two successive transpositions return the original matrix: (A^T)^T = A.
      • For any scalar k, (kA)^T = kA^T.
      • The transpose of a sum: (A + B)^T = A^T + B^T.

    Matrix Equality and Multiplication

    • Matrix Equality: Two matrices are equal if they have the same dimensions and matching corresponding entries.
    • Properties of Matrix Multiplication:
      • Associative property: A(BC) = AB(C).
      • Distributive property: A(B + C) = AB + AC and (A + B)C = AC + BC.

    Linear Equations and Graphs

    • Horizontal Line: Represented by the equation y = b.
    • Vertical Line: Represented by the equation x = a.
    • Point-Slope Form: y - y1 = m(x - x1), a formula for the equation of a line considering a point and its slope.
    • Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
    • Standard Form: The linear equation format Ax + By = C.

    Financial Applications

    • Linear Depreciation: V(t) = mt + b, where B is initial value, and M represents the depreciation rate.
    • Total Cost Function C(x): Represents costs as C(x) = (production cost per item)(quantity) + fixed cost, simplified to C(x) = mx + F.
    • Revenue Function R(x): The formula for revenue is R(x) = (price per item)(quantity), represented as R(x) = px.
    • Profit Function P(x): Profit is calculated as P(x) = R(x) - C(x).
    • Demand Function D(x): Typically linear with D(x) = mx + b, exhibiting a negative slope.
    • Supply Function S(x): Another linear function defined as S(x) = mx + b, with a positive slope.

    Systems of Equations

    • Independent System: Contains exactly one solution; characterized by M1 ≠ M2.
    • Inconsistent System: No solution exists; indicated by M1 = M2 with B1 ≠ B2.
    • Dependent System: Infinitely many solutions, where M1 = M2 and B1 = B2.
    • Break Even Point: Occurs where total revenue R(x) equals total cost C(x), represented by the ordered pair (break even quantity, break even revenue).
    • Equilibrium Point: Defined by where supply S(x) equals demand D(x), represented as (equilibrium quantity, equilibrium price).

    Reduced Row Echelon Form (RREF)

    • RREF Conditions:
      • All zero rows positioned below non-zero rows.
      • Each leading entry (first non-zero from the left) is 1 and is referred to as a leading 1.
      • Each leading 1 must be right of leading 1s in higher rows.
      • Each leading 1 is the only non-zero entry in its column.

    Pivoting

    • Pivoting: A technique to obtain a leading 1 in a specific location while converting all other entries in that column to zero.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your knowledge on matrix operations with these flashcards from TAMU MATH 140. Learn key concepts such as matrix addition, multiplication, and properties like commutative and associative. Perfect for exam preparation and understanding core mathematical principles related to matrices.

    More Quizzes Like This

    Matrix Operations
    6 questions

    Matrix Operations

    GoldenJadeite2644 avatar
    GoldenJadeite2644
    Matrix Operations and Inverse Matrices
    10 questions

    Matrix Operations and Inverse Matrices

    SpellbindingBalalaika avatar
    SpellbindingBalalaika
    Linear Algebra: Matrix Notation and Operations
    40 questions

    Linear Algebra: Matrix Notation and Operations

    FirmerBandoneon7262 avatar
    FirmerBandoneon7262
    Matrix Operations Quiz
    0 questions

    Matrix Operations Quiz

    EminentObsidian9783 avatar
    EminentObsidian9783
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser