12 Mid-Chapter Quiz

Do you know HOW?

Use matrices A, B, C, and D. Perform each operation.

A = [ 3 1 5 7 ] eh equals . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 1 , row2 column 1 , 5 , column 2 7 , end matrix

B = [ 4 6 1 0 ] b equals . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 6 , row2 column 1 , 1 , column 2 0 , end matrix

C = [ − 5 3 1 9 ] c equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 5 , column 2 3 , row2 column 1 , 1 , column 2 9 , end matrix

C = [ 1.5 2 9 − 6 ] c equals . matrix with 2 rows and 2 columns , row1 column 1 , 1.5 , column 2 2 , row2 column 1 , 9 , column 2 negative 6 , end matrix

1. A + C eh plus c
2. B − A b minus eh
3. 3D
4. BA
5. C(DB)
6. (AB)C

Solve each matrix equation.

7. X + [ − 3 2 9 − 7 ] = [ − 3 5 4 − 5 ] x plus . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 2 , row2 column 1 , 9 , column 2 negative 7 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 5 , row2 column 1 , 4 , column 2 negative 5 , end matrix
8. [ 4 − 6 − 7 2 ] − X = [ − 1 − 7 3 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 6 , row2 column 1 , negative 7 , column 2 2 , end matrix . minus x equals . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 negative 7 , row2 column 1 , 3 , column 2 negative 2 , end matrix
9. X − [ − 3 2 − 1 6 − 7 8 ] = [ − 2 3 5 1 − 3 7 ] x minus . matrix with 2 rows and 3 columns , row1 column 1 , negative 3 , column 2 2 , column 3 negative 1 , row2 column 1 , 6 , column 2 negative 7 , column 3 8 , end matrix . equals . matrix with 2 rows and 3 columns , row1 column 1 , negative 2 , column 2 3 , column 3 5 , row2 column 1 , 1 , column 2 negative 3 , column 3 7 , end matrix
10. 3 X + [ − 2 1 7 − 3 ] = [ 4 − 5 − 8 9 ] 3 x plus . matrix with 2 rows and 2 columns , row1 column 1 , negative 2 , column 2 1 , row2 column 1 , 7 , column 2 negative 3 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 5 , row2 column 1 , negative 8 , column 2 9 , end matrix
11. [ − 3 2 5 − 1 ] = [ 4 5 − 1 3 ] − 1 2 X . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 2 , row2 column 1 , 5 , column 2 negative 1 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 5 , row2 column 1 , negative 1 , column 2 3 , end matrix . minus , 1 half x

Solve each equation for x and y.

12. [ − 3 + 2 x 2 4 − 7 y ] = [ x − 4 2 4 − 35 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 plus 2 x , column 2 2 , row2 column 1 , 4 , column 2 negative 7 y , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , x minus 4 , column 2 2 , row2 column 1 , 4 , column 2 negative 35 , end matrix
13. [ 2 x 3 − 3 − 7 x + y ] = [ 3 x + 2 3 − 3 − 4 x ] . matrix with 2 rows and 2 columns , row1 column 1 , 2 x , column 2 3 , row2 column 1 , negative 3 , column 2 negative 7 x plus y , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 3 x plus 2 , column 2 3 , row2 column 1 , negative 3 , column 2 negative 4 x , end matrix

Evaluate the determinant of each matrix.

14. [ − 5 3 1 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 5 , column 2 3 , row2 column 1 , 1 , column 2 2 , end matrix
15. [ 3 − 1 4 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 negative 1 , row2 column 1 , 4 , column 2 2 , end matrix
16. [ − 3 2 0 − 2 1 5 − 1 0 2 ] . matrix with 3 rows and 3 columns , row1 column 1 , negative 3 , column 2 2 , column 3 0 , row2 column 1 , negative 2 , column 2 1 , column 3 5 , row3 column 1 , negative 1 , column 2 0 , column 3 2 , end matrix
17. [ 5 − 1 1 − 3 0 2 7 − 8 4 ] . matrix with 3 rows and 3 columns , row1 column 1 , 5 , column 2 negative 1 , column 3 1 , row2 column 1 , negative 3 , column 2 0 , column 3 2 , row3 column 1 , 7 , column 2 negative 8 , column 3 4 , end matrix

Find the inverse of each matrix, if it exists.

18. [ − 5 2 3 − 1 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 5 , column 2 2 , row2 column 1 , 3 , column 2 negative 1 , end matrix
19. [ 4 − 5 1 − 6 ] . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 5 , row2 column 1 , 1 , column 2 negative 6 , end matrix
20. [ − 1 3 3 1 5 1 2 4 − 3 ] . matrix with 3 rows and 3 columns , row1 column 1 , negative 1 , column 2 3 , column 3 3 , row2 column 1 , 1 , column 2 5 , column 3 1 , row3 column 1 , 2 , column 2 4 , column 3 negative 3 , end matrix
21. [ 3 − 1 2 − 1 0 2 1 3 − 1 ] . matrix with 3 rows and 3 columns , row1 column 1 , 3 , column 2 negative 1 , column 3 2 , row2 column 1 , negative 1 , column 2 0 , column 3 2 , row3 column 1 , 1 , column 2 3 , column 3 negative 1 , end matrix

Given the vertices, find the area of each triangle.

22. ( − 4 , 1 ) , open negative 4 comma 1 close comma  (5, 2), and ( 2 , − 3 ) open 2 comma negative 3 close
23. ( − 2 , − 3 ) , ( − 5 , 4 ) , open negative 2 comma negative 3 close comma open negative 5 comma 4 close comma  and (4, 1)

Do you UNDERSTAND?

24. Writing How can you decide whether you can multiply two matrices?
25. Open-Ended Write a matrix equation with solution [ 12 7 − 3 8 9 0 − 11 1 ] . . matrix with 2 rows and 4 columns , row1 column 1 , 12 , column 2 7 , column 3 negative 3 , column 4 8 , row2 column 1 , 9 , column 2 0 , column 3 negative 11 , column 4 1 , end matrix . .
26. Reasoning Suppose the product of two matrices has dimensions 4 × 3 . 4 times 3 .  If one of the matrices in the multiplication has dimensions 4 × 5 , 4 times 5 comma  what are the dimensions of the other matrix?
27. Sales A store sells three kinds of pencils and the first matrix below shows the prices, in dollars, for each type. The second matrix shows the quantity sold for each type. Explain how you can find the total sales using the two matrices.

Type A B C [ 3 4 2 ] Type A B C [ 20 10 15 ] table with 1 row and 2 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , table with 1 row and 4 columns , row1 column 1 , cap type , column 2 eh , column 3 b , column 4 c , end table , row2 column 1 , . matrix with 1 row and 3 columns , row1 column 1 , 3 , column 2 4 , column 3 2 , end matrix , end table , column 2 table with 2 rows and 1 column , row1 column 1 , cap type , row2 column 1 , table with 3 rows and 1 column , row1 column 1 , eh , row2 column 1 , b , row3 column 1 , c , end table . matrix with 3 rows and 1 column , row1 column 1 , 20 , row2 column 1 , 10 , row3 column 1 , 15 , end matrix , end table , end table

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