Algebra II Quiz 6 - 30 points



A. 39 Algebra II – Matrices on GC Name ___________________

Use the graphing calculator to multiply the following matrices or state why multiplication cannot be done.

Always use “normal English,” not “Calculator language.”

1. [A] = [pic] [B] = [pic] Find the product of [A] and [B].

On the graphing calculator, punch the following buttons to perform matrix multiplication:

(2nd) MATRIX 1[A] highlighted[pic]EDIT ENTER 2 ENTER x 2 ENTER

Then plug in the entries. Now hit 2nd QUIT

(2nd) MATRIX [pic]EDIT [pic]2[B] highlighted ENTER 2 ENTER x 2 ENTER

Then plug in the entries. Then hit 2nd QUIT

(2nd) MATRIX 1[A] ENTER times (2nd) MATRIX 2[B] ENTER

Record your answer here.

2. Use the same instructions to multiply these: [pic] =

3. [pic] =

4. Make the calculator do all of the work on this one. Plug in the first matrix as Matrix A and the second

one as Matrix B. Then hit [pic] times Matrix A plus 2 times matrix B. Don’t do any work by hand!

[pic]

5. [pic] What message did your calculator give you? What does this means?

What is the answer that you would have given if you were not using your calculator?

Try to plug in Matrix A = [pic] without looking back at the directions.

To find the determinant on the GC, use these directions:

(2nd) MATRIX 1[A] highlighted [pic] MATH 1:det( ENTER (2nd) MATRIX 1[A] ENTER ENTER .

6. Find the value of the determinant of Matrix A by hand to see if the GC gave you the correct answer.

Enter these matrices on your calculator:

A = [pic] B = [pic] C = [pic] D = [pic] E = [pic]

Find the determinant of each or explain (in normal English) why a determinant does not exist.

7. det [A]

8. det [B]

9. det [C]

10. det [D]

11. det [E]

Find the inverse of each matrix or state why the inverse does not exist. Use (2nd)MATRIX 1A (or whichever one you want) [pic] ENTER . (Change all entries from decimals to fractions.)

12. [pic] 13. [pic]

14. [pic] 15. [pic]

16. [pic] 17. [pic]

Use inverse matrices to solve these systems. First, write a matrix equation. The coefficients can be placed in matrix A and the column matrix of answers can be called matrix B. After plugging both in, just use MATRIX 1A [pic] TIMES MATRIX 2B ENTER

Show your set-up matrix equation and the answer step for each of the following.

18. [pic] 19. [pic]

20. [pic] 21. [pic]

22. [pic]

23. Solve for y in #22 using Cramer’s Rule and the GC. Show the set-ups for numerator and

denominator. Calculate each individual determinant and reduce your answer. Did you get the

same answer as you did in #22 above?

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