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Homework: Multiplying Matrices II

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides further practice problems related to multiplying matrices.

Exercise 1

Matrix [A][A] is 12341234 size 12{ left [ matrix { 1 {} # 2 {} ## 3 {} # 4{} } right ]} {}. Matrix [B][B] is 56785678 size 12{ left [ matrix { 5 {} # 6 {} ## 7 {} # 8{} } right ]} {}.

  • a. Find the product ABAB.
  • b. Find the product BABA.

Exercise 2

Multiply.

2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 size 12{ left [ matrix { 2 {} # 6 {} # 4 {} ## 9 {} # 5 {} # 8{} } right ]` left [ matrix { 2 {} # 5 {} # 4 {} # 7 {} ## 3 {} # 4 {} # 6 {} # 9 {} ## 8 {} # 4 {} # 2 {} # 0{} } right ]} {}

Exercise 3

Multiply.

2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 size 12{ left [ matrix { 2 {} # 5 {} # 4 {} # 7 {} ## 3 {} # 4 {} # 6 {} # 9 {} ## 8 {} # 4 {} # 2 {} # 0{} } right ]` left [ matrix { 2 {} # 6 {} # 4 {} ## 9 {} # 5 {} # 8{} } right ]} {}

Exercise 4

5 3 9 7 5 3 2 7 5 x y z 5 3 9 7 5 3 2 7 5 x y z size 12{ left [ matrix { 5 {} # 3 {} # 9 {} ## 7 {} # 5 {} # 3 {} ## 2 {} # 7 {} # 5{} } right ]` left [ matrix { x {} ## y {} ## z } right ]} {}

  • a. Multiply.
  • b. Now, multiply 53975327521055397532752105 size 12{ left [ matrix { 5 {} # 3 {} # 9 {} ## 7 {} # 5 {} # 3 {} ## 2 {} # 7 {} # 5{} } right ]` left [ matrix { 2 {} ## "10" {} ## 5 } right ]} {}—but not by manually multiplying it out! Instead, plug x = 2 x=2, y = 10 y=10, and z = 5 z=5 into the formula you came up with in part (a).

Exercise 5

Multiply.

1 2 3 4 5 6 7 8 9 1 0 0 0 1 0 0 0 1 1 2 3 4 5 6 7 8 9 1 0 0 0 1 0 0 0 1 size 12{ left [ matrix { 1 {} # 2 {} # 3 {} ## 4 {} # 5 {} # 6 {} ## 7 {} # 8 {} # 9{} } right ]` left [ matrix { 1 {} # 0 {} # 0 {} ## 0 {} # 1 {} # 0 {} ## 0 {} # 0 {} # 1{} } right ]} {}

Exercise 6

3 [ 3 -2 6 3 ] [ x y ] = [ 9 -3 ] 3[ 3 -2 6 3 ][ x y ]=[ 9 -3 ]

  • a. Find the x x and y y values that will make this matrix equation true.
  • b. Test your answer by doing the multiplication to make sure it works out.

Exercise 7

[ 1 2 3 4 ] [ Some Matrix ] = [ 1 2 3 4 ] [ 1 2 3 4 ][ Some Matrix ]=[ 1 2 3 4 ]

  • a. Find the “some matrix” that will make this matrix equation true.
  • b. Test your answer by doing the multiplication to make sure it works out.

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