Download Algebra II Quiz 6

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.”
2 3
1. [A] = 

0 1
4 0 
[B] = 
 Find the product of [A] and [B].
1 2 
On the graphing calculator, punch the following buttons to perform matrix multiplication:
(2nd) MATRIX 1[A] highlighted  EDIT ENTER 2 ENTER x 2 ENTER
Then plug in the entries. Now hit 2nd QUIT
(2nd) MATRIX  EDIT  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.
6 1
2 0 1 

2. Use the same instructions to multiply these: 
2 0 =


3 4 0  
3 5

3.
6 1 

 2 0 1 =
2
0

 3 4 0 



3 5

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 3 times Matrix A plus 2 times matrix B. Don’t do any work by hand!
20 17 13 22 

 

3 23
54  2 49 36

46 91 
 
50 57

3
 
5.  6 
 7 
 2
  0  What message did your calculator give you? What does this means?
 1 
What is the answer that you would have given if you were not using your calculator?
 2
Try to plug in Matrix A = 
3
4
without looking back at the directions.
6 
To find the determinant on the GC, use these directions:
(2nd) MATRIX 1[A] highlighted  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:
4 5 5 
3 1
4 1


6 0 
A = 
B = 
C = 2


2
4
8
2





3 7 1

4

D = 2

3
3
5
6
2 

0 
1

8 6
E = 
9 7
2 
3

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
1
whichever one you want) X
ENTER . (Change all entries from decimals to fractions.)
-1
12. A
-1
13. B
14. C-1
-1
15. D
-1
16. E
17. A  A
-1
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
1
in, just use MATRIX 1A X TIMES MATRIX 2B ENTER
Show your set-up matrix equation and the answer step for each of the following.
2x  5y  53
18. 
6x  7y  39
3x  5y  12
19. 
2x  3y  8
1.5x  0.2y  8.3
20. 
0.4x  0.4y  0.4
5x  2y  4
21. 
3x  4y  6
2x  3y  z  15

22. x  4z  10
2y  7z  45

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?