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Homework: Introduction to Matrices

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

Summary: This module provides practice problems which develop concepts related to matrices.

Exercise 1

In the following matrix…

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

  • a. What are the dimensions? __ ×× __
  • b. Copy the second column here:
  • c. Copy the third row here:
  • d. Write another matrix which is equal to this matrix.

Exercise 2

Add the following two matrices.

[ 2 6 4 9 n 8 ] + [ 5 7 1 9 -n 3n ] = [ 2 6 4 9 n 8 ]+[ 5 7 1 9 -n 3n ]=

Exercise 3

Add the following two matrices.

[ 2 6 4 9 n 8 ] + [ 5 7 9 -n ] = [ 2 6 4 9 n 8 ]+[ 5 7 9 -n ]=

Exercise 4

Subtract the following two matrices.

[ 2 6 4 9 n 8 ] - [ 5 7 1 9 -n 3n ] = [ 2 6 4 9 n 8 ]-[ 5 7 1 9 -n 3n ]=

Exercise 5

Solve the following equation for x x and y y. (That is, find what x x and y y must be for this equation to be true.)

[ 2x 5y ] + [ x+y -6x ] = [ 6 2 ] [ 2x 5y ]+[ x+y -6x ]=[ 6 2 ]

Exercise 6

Solve the following equation for x x and y y. (That is, find what x x and y y must be for this equation to be true.)

x + y 3x − 2y + 4x − y x + 5y = 3 5 7 9 x + y 3x − 2y + 4x − y x + 5y = 3 5 7 9 size 12{ left [ matrix { x+y {} ## 3x - 2y } right ]+ left [ matrix { 4x - y {} ## x+5y } right ]= left [ matrix { 3 {} # 5 {} ## 7 {} # 9{} } right ]} {}

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