• Step 1 Write 4 × 2 4 times 2  matrices to show the information from the two tables.

  Let  A =  the first half records  cap let eh equals . thefirsthalfrecords

  B =  the  second  half records  b equals , the . second . halfrecords

  F =  the final records  f equals . thefinalrecords

  A = [ 30 11 29 12 25 16 24 17 ] F = [ 53 29 67 15 58 24 61 21 ] eh equals left bracket . table with 4 rows and 2 columns , row1 column 1 , 30 , column 2 11 , row2 column 1 , 29 , column 2 12 , row3 column 1 , 25 , column 2 16 , row4 column 1 , 24 , column 2 17 , end table . right bracket f equals left bracket . table with 4 rows and 2 columns , row1 column 1 , 53 , column 2 29 , row2 column 1 , 67 , column 2 15 , row3 column 1 , 58 , column 2 24 , row4 column 1 , 61 , column 2 21 , end table . right bracket

  Think

  What are the dimensions of matrix B?

  B will have 4 rows and 2 columns. It is a 4 × 2 4 times 2  matrix.

• Step 2 Solve A + B = F eh plus b equals f  for B.

  B = F − A b equals f minus eh

  B = [ 53 29 67 15 58 24 61 21 ] − [ 30 11 29 12 25 16 24 17 ] = [ 53 − 30 29 − 11 67 − 29 15 − 12 58 − 25 24 − 16 61 − 24 21 − 17 ] = [ 23 18 38 3 33 8 37 4 ] b equals left bracket . table with 4 rows and 2 columns , row1 column 1 , 53 , column 2 29 , row2 column 1 , 67 , column 2 15 , row3 column 1 , 58 , column 2 24 , row4 column 1 , 61 , column 2 21 , end table . right bracket minus left bracket . table with 4 rows and 2 columns , row1 column 1 , 30 , column 2 11 , row2 column 1 , 29 , column 2 12 , row3 column 1 , 25 , column 2 16 , row4 column 1 , 24 , column 2 17 , end table . right bracket equals left bracket . table with 4 rows and 2 columns , row1 column 1 , 53 minus 30 , column 2 29 minus 11 , row2 column 1 , 67 minus 29 , column 2 15 minus 12 , row3 column 1 , 58 minus 25 , column 2 24 minus 16 , row4 column 1 , 61 minus 24 , column 2 21 minus 17 , end table . right bracket equals left bracket . table with 4 rows and 2 columns , row1 column 1 , 23 , column 2 18 , row2 column 1 , 38 , column 2 3 , row3 column 1 , 33 , column 2 8 , row4 column 1 , 37 , column 2 4 , end table . right bracket

  Team 2 had the best record (38 wins and 3 losses) during the second half of the season.

✓ Got It?

2. If B = [ 1 6 − 1 2 6 1 − 1 − 2 4 ] , C = [ 2 0 0 − 1 − 3 6 2 3 − 1 ] , b equals left bracket . table with 3 rows and 3 columns , row1 column 1 , 1 , column 2 6 , column 3 negative 1 , row2 column 1 , 2 , column 2 6 , column 3 1 , row3 column 1 , negative 1 , column 2 negative 2 , column 3 4 , end table . right bracket . comma . c equals left bracket . table with 3 rows and 3 columns , row1 column 1 , 2 , column 2 0 , column 3 0 , row2 column 1 , negative 1 , column 2 negative 3 , column 3 6 , row3 column 1 , 2 , column 2 3 , column 3 negative 1 , end table . right bracket comma  and A − B = C , eh minus b equals c comma  what is A?

Problem 3 Using Identity and Opposite Matrices

What are the following sums?

1. [ 1 2 5 − 7 ] + [ 0 0 0 0 ] = [ 1 + 0 2 + 0 5 + 0 − 7 + 0 ] = [ 1 2 5 − 7 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , 1 , column 2 2 , row2 column 1 , 5 , column 2 negative 7 , end table . right bracket plus left bracket . table with 2 rows and 2 columns , row1 column 1 , 0 , column 2 0 , row2 column 1 , 0 , column 2 0 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 1 plus 0 , column 2 2 plus 0 , row2 column 1 , 5 plus 0 , column 2 negative 7 plus 0 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 1 , column 2 2 , row2 column 1 , 5 , column 2 negative 7 , end table . right bracket
2. [ 2 8 − 3 0 ] + [ − 2 − 8 3 0 ] = [ 2 + ( − 2 ) 8 + ( − 8 ) − 3 + 3 0 + 0 ] = [ 0 0 0 0 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 , column 2 8 , row2 column 1 , negative 3 , column 2 0 , end table . right bracket plus left bracket . table with 2 rows and 2 columns , row1 column 1 , negative 2 , column 2 negative 8 , row2 column 1 , 3 , column 2 0 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 2 plus open negative 2 close , column 2 8 plus open negative 8 close , row2 column 1 , negative 3 plus 3 , column 2 0 plus 0 , end table . right bracket equals left bracket . table with 2 rows and 2 columns , row1 column 1 , 0 , column 2 0 , row2 column 1 , 0 , column 2 0 , end table . right bracket

✓ Got It?

3. What are the following sums?
   1. [ 14 5 0 − 2 ] + [ − 14 − 5 0 2 ] left bracket . table with 2 rows and 2 columns , row1 column 1 , 14 , column 2 5 , row2 column 1 , 0 , column 2 negative 2 , end table . right bracket plus left bracket . table with 2 rows and 2 columns , row1 column 1 , negative 14 , column 2 negative 5 , row2 column 1 , 0 , column 2 2 , end table . right bracket
   2. [ 0 0 0 0 0 0 ] + [ − 1 10 − 5 0 2 − 3 ] left bracket . table with 2 rows and 3 columns , row1 column 1 , 0 , column 2 0 , column 3 0 , row2 column 1 , 0 , column 2 0 , column 3 0 , end table . right bracket plus left bracket . table with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 10 , column 3 negative 5 , row2 column 1 , 0 , column 2 2 , column 3 negative 3 , end table . right bracket