Take Note Properties: Properties of Matrix Addition

If A, B, and C are m × n m times n  matrices, then

Problem 4 Finding Unknown Matrix Values

Multiple Choice What values of x and y make the equation true?

[ 9 3 x + 1 2 y − 1 10 ] = [ 9 16 − 5 10 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , 9 , column 2 3 x plus 1 , row2 column 1 , 2 y minus 1 , column 2 10 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 9 , column 2 16 , row2 column 1 , negative 5 , column 2 10 , end table . right bracket

1. x = 3 , y = 5 x equals 3 comma y equals 5
2. x = 17 3 , y = 5 x equals , 17 over 3 . comma y equals 5
3. x = 5 , y = − 2 x equals 5 comma y equals negative 2
4. x = 5 , y = − 3 x equals 5 comma y equals negative 3

3 x + 1 = 16 Set corresponding elements equal  . 2 y − 1 = − 5 3 x = 16 − 1 Isolate the variable term  . 2 y = − 5 + 1 3 x = 15 Simplify. 2 y = − 4 x = 5 Solve for  x  and  y . y = − 2 table with 4 rows and 5 columns , row1 column 1 , 3 x plus 1 , column 2 equals 16 , column 3 cap setcorrespondingelementsequal . . , column 4 2 y minus 1 , column 5 equals negative 5 , row2 column 1 , 3 x , column 2 equals 16 minus 1 , column 3 cap isolatethevariableterm . . , column 4 2 y , column 5 equals negative 5 plus 1 , row3 column 1 , 3 x , column 2 equals 15 , column 3 cap simplify. , column 4 2 y , column 5 equals negative 4 , row4 column 1 , x , column 2 equals 5 , column 3 cap solvefor . x , and , y . , column 4 y , column 5 equals negative 2 , end table

The correct answer is C.

✓ Got It?

4. What values of x, y, and z make the following equations true?
   1. [ x + 3 − 2 y − 1 x + 1 ] = [ 9 − 2 2 y + 5 7 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , x plus 3 , column 2 negative 2 , row2 column 1 , y minus 1 , column 2 x plus 1 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 9 , column 2 negative 2 , row2 column 1 , 2 y plus 5 , column 2 7 , end table . right bracket
   2. [ z − 3 3 x 0 ] − [ 10 − 4 x 2 y + 6 ] = [ 2 1 8 4 y + 12 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , z , column 2 negative 3 , row2 column 1 , 3 x , column 2 0 , end table . right bracket minus left bracket . table with 2 rows and 2 columns , row1 column 1 , 10 , column 2 negative 4 , row2 column 1 , x , column 2 2 y plus 6 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 , column 2 1 , row2 column 1 , 8 , column 2 4 y plus 12 , end table . right bracket