Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each matrix equation. If an equation cannot be solved, explain why.

7. [ 12 7 5 3 ] X = [ 2 − 1 3 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 12 , column 2 7 , row2 column 1 , 5 , column 2 3 , end matrix x equals . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 negative 1 , row2 column 1 , 3 , column 2 2 , end matrix
8. [ 0 − 4 0 − 1 ] X = [ 0 4 ] . matrix with 2 rows and 2 columns , row1 column 1 , 0 , column 2 negative 4 , row2 column 1 , 0 , column 2 negative 1 , end matrix x equals , matrix with 2 rows and 1 column , row1 column 1 , 0 , row2 column 1 , 4 , end matrix
9. [ 5 1 4 2 − 3 − 5 7 2 − 6 ] X = [ 5 2 5 ] . matrix with 3 rows and 3 columns , row1 column 1 , 5 , column 2 1 , column 3 4 , row2 column 1 , 2 , column 2 negative 3 , column 3 negative 5 , row3 column 1 , 7 , column 2 2 , column 3 negative 6 , end matrix x equals . matrix with 3 rows and 1 column , row1 column 1 , 5 , row2 column 1 , 2 , row3 column 1 , 5 , end matrix
10. [ 6 10 13 4 − 2 7 0 9 − 8 ] X = [ 84 18 56 ] . matrix with 3 rows and 3 columns , row1 column 1 , 6 , column 2 10 , column 3 13 , row2 column 1 , 4 , column 2 negative 2 , column 3 7 , row3 column 1 , 0 , column 2 9 , column 3 negative 8 , end matrix x equals . matrix with 3 rows and 1 column , row1 column 1 , 84 , row2 column 1 , 18 , row3 column 1 , 56 , end matrix

See Problem 2.

Write each system as a matrix equation. Identify the coefficient matrix, the variable matrix, and the constant matrix.

11. { x + y = 5 x − 2 y = − 4 left brace . table with 2 rows and 2 columns , row1 column 1 , x plus y equals , column 2 5 , row2 column 1 , x minus 2 y equals , column 2 negative 4 , end table
12. { y = 3 x − 7 x = 2 left brace . table with 2 rows and 1 column , row1 column 1 , y equals 3 x minus 7 , row2 column 1 , x equals 2 , end table
13. { 3 a + 5 b = 0 a + b = 2 left brace . table with 2 rows and 1 column , row1 column 1 , 3 eh plus 5 b equals 0 , row2 column 1 , eh plus b equals 2 , end table
14. { x + 3 y − z = 2 x + 2 z = 8 2 y − z = 1 left brace . table with 3 rows and 3 columns , row1 column 1 , x plus 3 y minus , column 2 z , column 3 equals 2 , row2 column 1 , x plus , column 2 2 z , column 3 equals 8 , row3 column 1 , 2 y minus , column 2 z , column 3 equals 1 , end table
15. { r − s + t = 150 2 r + t = 425 s + 3 t = 0 left brace . table with 3 rows and 2 columns , row1 column 1 , r minus s plus t equals , column 2 150 , row2 column 1 , 2 r plus t equals , column 2 425 , row3 column 1 , s plus 3 t equals , column 2 0 , end table
16. { x + 2 y = 11 2 x + 3 y = 18 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 2 y equals 11 , row2 column 1 , 2 x plus 3 y equals 18 , end table

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