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0. Review of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

1. Equations & Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs of Equations(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

Dividing Polynomials
(0)

Zeros of Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential & Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Systems of Equations & Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

8. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

9. Sequences, Series, & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

10. Combinatorics & Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

7. Systems of Equations & Matrices

Introduction to Matrices

7. Systems of Equations & Matrices

Introduction to Matrices: Videos & Practice Problems

Video Lessons Practice Worksheet

200 problems

Problem types you want to practice:

Problem 31Multiple Choice

Perform the following matrix operation: A - B

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Problem 32Multiple Choice

Perform the following matrix operation: A + B

Matrix A with values 7, 2, 6, 8.

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Problem 33Multiple Choice

Find the given matrices (if possible):

a. PQ

b. QP

Matrices P and Q for the introduction to matrices in college algebra.

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Problem 34Multiple Choice

Find the given matrices (if possible):

a. PQ

b. QP

Matrices P and Q for the introduction to matrices in college algebra.

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Problem 35Multiple Choice

Find the given matrices (if possible):

a. PQ

b. QP

Matrices P and Q for the introduction to matrices in college algebra.

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Problem 36Multiple Choice

Find the given matrices (if possible):

a. PQ

b. QP

Matrices P and Q with values for the introduction to matrices topic.

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Problem 37Multiple Choice

Find the given matrices (if possible):

a. PQ

b. QP

Matrices P and Q defined for the introduction to matrices topic in college algebra.

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Problem 38Multiple Choice

To make the matrices in the question equal, determine values for the variables.

Matrix equation showing variables y, x, and z to solve for equality in college algebra.

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Problem 39Multiple Choice

To make the matrices in the question equal, determine values for the variables.

Matrix equation showing x and y values to solve for equality.

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Problem 40Multiple Choice

If A = [a_ij], find a₁₄ and a₃₁ and state the matrix's order. If identification is not possible, state why.

Matrix A with elements shown, order 3x4, for college algebra systems of equations.

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Problem 41Multiple Choice

If A = [a_ij], find a₁₃ and a₃₁ and state the matrix's order. If identification is not possible, state why.

Matrix A with elements [-5, 2, 3] and [1, -3, 7], illustrating systems of equations.

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Problem 42Multiple Choice

Determine the augmented matrix that corresponds to the system of equations shown:

System of equations for college algebra, chapter 7, introduction to matrices.

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Problem 43Multiple Choice

Write a new matrix after applying mentioned row operations

Matrix showing row operations applied to a system of equations.

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Problem 44Multiple Choice

Find the number of rows and columns in the following matrix. Also, find the dimension of the matrix.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"[\" close=\"]\"><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>6</mn></mtd><mtd><mn>9</mn></mtd><mtd><mn>10</mn></mtd><mtd><mn>11</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>13</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>6</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

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Problem 45Multiple Choice

Determine the augmented matrix that corresponds to the system of equations shown:

System of equations for determining the augmented matrix.

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Problem 46Multiple Choice

Using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices.

System of equations for Gaussian elimination: x+y+z=1, 3x+2y+z=4, 6x-y+3z=2.

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Problem 47Multiple Choice

Write the augmented matrix for the system of linear equations given below.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>9</mn><mi>y</mi><mo>=</mo><mn>11</mn><mspace linebreak=\"newline\"></mspace><mn>10</mn><mi>x</mi><mo>+</mo><mn>13</mn><mi>y</mi><mo>=</mo><mn>16</mn></mstyle></math>","truncated":false}$

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Problem 48Multiple Choice

Using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices.

System of equations for Gaussian elimination: 2x + y + z = 6, 3x + y = 3, 2x - 3y = 2.

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Problem 49Multiple Choice

By using Gaussian elimination or Gauss-Jordan elimination, provide a solution for the following system of equations using matrices. System of equations for Gaussian elimination in college algebra, chapter 7, introduction to matrices.

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Problem 50Multiple Choice

Determine the augmented matrix that corresponds to the system of equations shown:

System of equations for the introduction to matrices topic in college algebra.

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Problem 51Multiple Choice

Apply the indicated row transformation to the following matrix.

Add the result -5 times of row 1 to row 2

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Problem 52Multiple Choice

Determine the augmented matrix that corresponds to the system of equations shown:

System of equations for determining the augmented matrix.

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Problem 53Multiple Choice

Apply the indicated row transformation to the following matrix.

Add the result -10 times of row 1 to row 2

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Problem 54Multiple Choice

Determine the system of linear equations associated to the following augmented matrix. Use the variables x, y, and z.

Augmented matrix representing a system of linear equations for x, y, z.

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Problem 55Multiple Choice

Apply the indicated row transformation to the following matrix.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"[\" close=\"]\"><mtable><mtr><mtd><mn>8</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>8</mn></mtd></mtr><mtr><mtd><mn>12</mn></mtd><mtd><mn>11</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

Add the result 6 times of row 1 to row 2

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Problem 56Multiple Choice

Apply the indicated row transformation to the following matrix.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"[\" close=\"]\"><mtable><mtr><mtd><mn>5</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>10</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>6</mn></mtd><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

Add the result 8 times of row 1 to row 2

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Problem 57Multiple Choice

Determine the system of linear equations associated to the following augmented matrix. Use the variables w, x, y, and z.

Augmented matrix for a system of linear equations with variables w, x, y, z.

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Problem 58Multiple Choice

What is the augmented matrix for the following system of equations? Also, state the dimension of the matrix. Please note that you don't need to solve it.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>4</mn><mi>z</mi><mo>-</mo><mn>7</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>6</mn><mi>x</mi><mo>-</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>11</mn><mi>z</mi><mo>+</mo><mn>13</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>9</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn><mi>z</mi><mo>-</mo><mn>12</mn><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$

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Problem 59Multiple Choice

Write the new matrix after performing the matrix row operation.

Matrix before row operation in college algebra, chapter 7, introduction to matrices.

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Problem 60Multiple Choice

What is the augmented matrix for the following system of equations? Also, state the dimension of the matrix. Please note that you don't need to solve it.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"{\" close=\"\"><mtable columnalign=\"left\"><mtr><mtd><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>5</mn><mi>z</mi><mo>-</mo><mn>6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>7</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>10</mn><mi>z</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>8</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>13</mn><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}$