Problem 1 Adding and Subtracting Matrices

Given  C = [ 3 2 4 − 1 4 0 ] cap given c equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 3 , column 2 2 , column 3 4 , row2 column 1 , negative 1 , column 2 4 , column 3 0 , end table . right bracket  and D = [ 1 4 3 − 2 2 4 ] , d equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 1 , column 2 4 , column 3 3 , row2 column 1 , negative 2 , column 2 2 , column 3 4 , end table . right bracket comma  what are the following?

1. C + D c plus d

   [ 3 2 4 − 1 4 0 ] + [ 1 4 3 − 2 2 4 ] = [ 3 + 1 2 + 4 4 + 3 − 1 + ( − 2 ) 4 + 2 0 + 4 ] = [ 4 6 7 − 3 6 4 ] table with 3 rows and 1 column , row1 column 1 , left bracket . table with 2 rows and 3 columns , row1 column 1 , 3 , column 2 2 , column 3 4 , row2 column 1 , negative 1 , column 2 4 , column 3 0 , end table . right bracket plus left bracket . table with 2 rows and 3 columns , row1 column 1 , 1 , column 2 4 , column 3 3 , row2 column 1 , negative 2 , column 2 2 , column 3 4 , end table . right bracket , row2 column 1 , equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 3 plus 1 , column 2 2 plus 4 , column 3 4 plus 3 , row2 column 1 , negative 1 plus open negative 2 close , column 2 4 plus 2 , column 3 0 plus 4 , end table . right bracket , row3 column 1 , equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 4 , column 2 6 , column 3 7 , row2 column 1 , negative 3 , column 2 6 , column 3 4 , end table . right bracket , end table

2. C − D c minus d

   [ 3 2 4 − 1 4 0 ] − [ 1 4 3 − 2 2 4 ] = [ 3 − 1 2 − 4 4 − 3 − 1 − ( − 2 ) 4 − 2 0 − 4 ] = [ 2 − 2 1 1 2 − 4 ] table with 3 rows and 1 column , row1 column 1 , left bracket . table with 2 rows and 3 columns , row1 column 1 , 3 , column 2 2 , column 3 4 , row2 column 1 , negative 1 , column 2 4 , column 3 0 , end table . right bracket minus left bracket . table with 2 rows and 3 columns , row1 column 1 , 1 , column 2 4 , column 3 3 , row2 column 1 , negative 2 , column 2 2 , column 3 4 , end table . right bracket , row2 column 1 , equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 3 minus 1 , column 2 2 minus 4 , column 3 4 minus 3 , row2 column 1 , negative 1 minus open negative 2 close , column 2 4 minus 2 , column 3 0 minus 4 , end table . right bracket , row3 column 1 , equals left bracket . table with 2 rows and 3 columns , row1 column 1 , 2 , column 2 negative 2 , column 3 1 , row2 column 1 , 1 , column 2 2 , column 3 negative 4 , end table . right bracket , end table

✓ Got It?

1. Given  A = [ − 12 24 − 3 5 − 1 10 ] cap given eh equals left bracket . table with 3 rows and 2 columns , row1 column 1 , negative 12 , column 2 24 , row2 column 1 , negative 3 , column 2 5 , row3 column 1 , negative 1 , column 2 10 , end table . right bracket  and B = [ − 3 1 2 − 4 − 1 5 ] , b equals left bracket . table with 3 rows and 2 columns , row1 column 1 , negative 3 , column 2 1 , row2 column 1 , 2 , column 2 negative 4 , row3 column 1 , negative 1 , column 2 5 , end table . right bracket comma  what are the following?
   1. A + B eh plus b
   2. A − B eh minus b
   3. Reasoning Is matrix addition commutative? Explain.

Problem 2 Solving a Matrix Equation

Sports The first table shows the teams with the four best records halfway through their season. The second table shows the full season records for the same four teams. Which team had the best record during the second half of the season?