Algebra 2 Chapter 3 Test Review

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Questions and Answers

What are the dimensions of a matrix with 3 rows and 4 columns?

  • 4 x 3
  • 3 x 4 (correct)
  • 4 x 4
  • 3 x 3

What is the solution to the system of equations 3x + 4y = 8 and x - 3y = -6?

(0, 2)

The system of linear equations has a solution of (2, 4). This is found using ___ method.

substitution

What is the solution to the system of equations 5x - 2y = 4 and -2y + x = 12?

<p>(-2, -7)</p> Signup and view all the answers

What is the solution for b in the equations a - 4b + c = 3, b - 3c = 10, and 3b - 8c = 24?

<p>-8</p> Signup and view all the answers

What is the cost of the SODAS in the problem?

<p>$2.50</p> Signup and view all the answers

What is the result of the matrix expression [-3 27] and [9 12]?

<p>Cannot determine from the given data.</p> Signup and view all the answers

What is the result of adding the matrix [-8]?

<p>Cannot determine from the given data.</p> Signup and view all the answers

What is the product of the matrices [-12 17] and [82 26]?

<p>Cannot determine from the given data.</p> Signup and view all the answers

What is the result of finding the product that is undefined?

<p>Undefined</p> Signup and view all the answers

What is the determinant evaluated to be?

<p>-34</p> Signup and view all the answers

What is the determinant when evaluated using diagonals?

<p>-44</p> Signup and view all the answers

Use Cramer's Rule to solve for y in the equations 3x - y = 0 and 5x + 2y = 22. What do you get for y?

<p>6</p> Signup and view all the answers

Use Cramer's Rule to solve for x in the system of equations. What is x?

<p>2</p> Signup and view all the answers

Find the inverse of the matrix [13 5][-5 -2]. What is the inverse?

<p>Cannot determine from the given data.</p> Signup and view all the answers

What is the inverse of the specified matrix where no inverse exists?

<p>none</p> Signup and view all the answers

Use a matrix equation to solve for (2, 1). What is the context?

<p>Cannot determine from the given data.</p> Signup and view all the answers

Solve the system of inequalities y ≤ 2x + 3 and y < ¹/₃x + 5. What is the solution?

<p>Cannot determine from the given data.</p> Signup and view all the answers

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Study Notes

Matrix Dimensions

  • A matrix with 3 rows and 4 columns is referred to as a 3 x 4 matrix.

System of Equations - Graphing

  • The point (0, 2) is the solution for the system:
    • 3x + 4y = 8
    • x - 3y = -6

Time Duration

  • A reference to 4 hours, potentially indicating the duration of an activity or event relevant to problem-solving in context.

System of Equations - Substitution

  • The point (2, 4) is obtained by solving the equations:
    • x + y = 6
    • 3x - 2y = -2 using the substitution method.

System of Equations - Elimination

  • The solution (-2, -7) arises from the elimination method applied to:
    • 5x - 2y = 4
    • -2y + x = 12.

Solution to Inequalities

  • The inequality system yields solutions satisfying:
    • y < 2x - 3
    • y ≥ 4.

Solving Linear Equations for b

  • The value of b is found to be -8 from the equations:
    • a - 4b + c = 3
    • b - 3c = 10
    • 3b - 8c = 24.

Price of Sodas

  • The cost of sodas in the related problem is $2.50.

Matrix Expression Solution

  • To find the solution for the matrix expression:
    • [-3 27]
    • [ 9 12], specific calculations on the matrix must be applied.

Addition/Subtraction Result

  • The result of adding and/or subtracting the identified matrix is noted as:
    • [-8].

Matrix Product Calculation

  • The product of the given matrices:
    • [-12 17]
    • [82 26] requires matrix multiplication techniques.

Undefined Matrix Product

  • The product of the indicated matrices results in an undefined outcome, suggesting matrix compatibility issues.

Determinant Evaluation

  • The determinant calculated for a specific matrix is -34.

Determinant with Diagonal Method

  • Evaluating the determinant using the diagonal cross-product method yields -44.

Cramer’s Rule for y

  • Using Cramer’s Rule, the value for y is determined to be 6 from the equations:
    • 3x - y = 0
    • 5x + 2y = 22.

Cramer’s Rule for x

  • Applying Cramer’s Rule, the value for x is concluded to be 2.

Inverse of a Matrix

  • The inverse of the matrix:
    • [13 5]
    • [-5 -2] can be found through matrix inversion techniques.

No Inverse Existence

  • Investigations into the matrix reveal it has no inverse.

Matrix Equation Solution

  • The solution to the matrix equation results in the ordered pair (2, 1).

System of Inequalities Solution

  • The inequalities yield solutions satisfying:
    • y ≤ 2x + 3
    • y < ¹/₃x + 5.

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