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Introduction to Matrices Practice Problems

Practice Problem #1

Find the order of the following matrices by dragging the order and droping into the correct matrix.

Matrices:

  1. the 2 by 1 column matrix 1 4
  2. the 3 by 2 matrix Row-: 1 5 6 Row-: 2 9 7 Row-: 3 2 1
  3. [25]
  4. the 1 by 2 row matrix 6 3
  5. the 3 by 3 matrix Row-: 1 2 negative 1 0 Row-: 2 7 4 negative 3 Row-: 3 1 9 5
  6. the 2 by 3 matrix Row-: 1 14 17 21 Row-: 2 25 11 19

Order of the Matrices:

  • 3x3
  • 2x1
  • 2x3
  • 3x2
  • 1x2
  • 1x1

Answers:

  1. the 2 by 1 column matrix 1 4

    Answer: 2x1

  2. the 3 by 2 matrix Row-: 1 5 6 Row-: 2 9 7 Row-: 3 2 1

    Answer: 3x2

  3. [25]

    Answer: 1x1

  4. the 1 by 2 row matrix 6 3

    Answer: 1x2

  5. the 3 by 3 matrix Row-: 1 2 negative 1 0 Row-: 2 7 4 negative 3 Row-: 3 1 9 5

    Answer: 3x3

  6. the 2 by 3 matrix Row-: 1 14 17 21 Row-: 2 25 11 19

    Answer: 2x3

Practice Problem #2

Use matrix M to find the following entries

M equals the 4 by 4 matrix Row-: 1Column-,- 1 2 Column-,- 2 6 Column-,- 3 11 Column-,- 4 18 Row-: 2Column-,- 1 9 Column-,- 2 14 Column-,- 3 7 Column-,- 4 13 Row-: 3Column-,- 1 17 Column-,- 2 5 Column-,- 3 0 Column-,- 4 19 Row-: 4Column-,- 1 12 Column-,- 2 10 Column-,- 3 1 Column-,- 4 4

m24 =

m21 =

m43 =

m33 =

m12 =

m32 =

Practice Problem #3

Given Matrix A find 5A.

A equals the 2 by 2 matrix Row-: 1 negative 2 6 Row-: 2 3 negative 4
5 A equals 5 times the 2 by 2 matrix Row-: 1 negative 2 6 Row-: 2 3 negative 4
5A equals a 2 by 2 matrix. Row 1 is blank times negative two and blank times 6. Row 2 is blank times 3 and blank times negative 4.

5A = 2 by 2 matrix Row 1: blank blank Row 2: blank blank

Practice Problem #4

Solve: 2 [1 4]
Choose the correct answer.

[6 3]

[8 4]

[2 5]

[2 8]

Practice Problem #5

Use scalar multiplication to solve the following matrices.

4 times the 2 by 2 matrix Row-: 1 3 0 Row-: 2 7 0

Choose the correct answer.

the 2 by 2 matrix Row-: 1 73 7 Row-: 2 96 5
the 2 by 2 matrix Row-: 1 12 0 Row-: 2 28 0
the 2 by 2 matrix Row-: 1 52 7 Row-: 2 36 5
the 2 by 2 matrix Row-: 1 39 7 Row-: 2 57 6