Algebra 2 Chapter 3 Test Review

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.