Problem 1 Identifying a Matrix Element

GRIDDED RESPONSE

What is element a 23 eh sub 23  in matrix A?

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a 23 eh sub 23  is 8.

✓ Got It?

1. What is element a 13 eh sub 13  in matrix A?

Problem 2 Representing Systems With Matrices

How can you represent the system of equations with a matrix?

1. { 2 x + y = 9 x − 6 y = − 1 left brace . table with 2 rows and 3 columns , row1 column 1 , 2 x plus , column 2 y equals , column 3 9 , row2 column 1 , x minus , column 2 6 y equals , column 3 negative 1 , end table

   The matrix [ 2 1 9 1 − 6 − 1 ] . matrix with 2 rows and 3 columns , row1 column 1 , 2 , column 2 1 , column 3 9 , row2 column 1 , 1 , column 2 negative 6 , column 3 negative 1 , end matrix  represents the system above.

   Think

   Why is the order of elements important in a matrix?

   Different orders of elements could correspond to different systems of equations.

2. { x − 3 y + z = 6 x + 3 z = 12 y = − 5 x + 1 left brace . table with 3 rows and 1 column , row1 column 1 , x minus 3 y plus z equals 6 , row2 column 1 , x plus 3 z equals 12 , row3 column 1 , y equals negative 5 x plus 1 , end table

• Step 1 Write each equation in the same variable order. Line up the variables. Leave space where a coefficient is 0.

  { x − 3 y + z = 6 x + 3 z = 12 5 x + y = 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 3 y plus , column 3 z equals , column 4 6 , row2 column 1 , x , column 2 plus , column 3 3 z equals , column 4 12 , row3 column 1 , 5 x plus , column 2 y , column 3 equals , column 4 1 , end table

• Step 2 Write the matrix using the coefficients and constants. Notice the 1's and 0's.

  [ 1 − 3 1 6 1 0 3 12 5 1 0 1 ] . matrix with 3 rows and 4 columns , row1 column 1 , 1 , column 2 negative 3 , column 3 1 , column 4 6 , row2 column 1 , 1 , column 2 0 , column 3 3 , column 4 12 , row3 column 1 , 5 , column 2 1 , column 3 0 , column 4 1 , end matrix