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0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & 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

Introduction to Matrices Practice Problems

193 problems

31PRACTICE PROBLEM

Perform the following matrix operation: A - B

32PRACTICE PROBLEM

Perform the following matrix operation: A + B

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

33PRACTICE PROBLEM

Find the given matrices (if possible):

a. PQ

b. QP

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

34PRACTICE PROBLEM

Find the given matrices (if possible):

a. PQ

b. QP

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

35PRACTICE PROBLEM

Find the given matrices (if possible):

a. PQ

b. QP

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

views

36PRACTICE PROBLEM

Find the given matrices (if possible):

a. PQ

b. QP

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

37PRACTICE PROBLEM

Find the given matrices (if possible):

a. PQ

b. QP

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

38PRACTICE PROBLEM

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.

39PRACTICE PROBLEM

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

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

40PRACTICE PROBLEM

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.

41PRACTICE PROBLEM

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.

42PRACTICE PROBLEM

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

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

43PRACTICE PROBLEM

Write a new matrix after applying mentioned row operations

Matrix showing row operations applied to a system of equations.

44PRACTICE PROBLEM

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

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

45PRACTICE PROBLEM

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

System of equations for determining the augmented matrix.

46PRACTICE PROBLEM

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.

47PRACTICE PROBLEM

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

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

48PRACTICE PROBLEM

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.

49PRACTICE PROBLEM

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.

50PRACTICE PROBLEM

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

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

51PRACTICE PROBLEM

Apply the indicated row transformation to the following matrix.

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

52PRACTICE PROBLEM

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

System of equations for determining the augmented matrix.

53PRACTICE PROBLEM

Apply the indicated row transformation to the following matrix.

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

54PRACTICE PROBLEM

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.

55PRACTICE PROBLEM

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

56PRACTICE PROBLEM

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

57PRACTICE PROBLEM

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.

58PRACTICE PROBLEM

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.

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

59PRACTICE PROBLEM

Write the new matrix after performing the matrix row operation.

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

60PRACTICE PROBLEM

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.

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

Two Variable Systems of Linear Equations Practice Problems Determinants and Cramer's Rule Practice Problems

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