8.4. Matrix Algebra http://www.ck12.org
Notice how the matrix transformation rotates graphs in a counterclockwise direction 90◦.
[x y][cos 90◦ sin 90◦
−sin 90 cos 90
]
=[−y x]The matrix transformation applied in the following order will rotate a graph clockwise 90◦.
[cos 90◦ sin 90◦
−sin 90 cos 90][x
y]
=
[y
−x]
Practice
Do #1-#11 without your calculator.
A=
[2 7
3 8
]
,B=
[0 5 1
3 4 6
]
,C=
[14 6
1 2
]
,D=
[5 0
1 2
]
- FindAC. If not possible, explain.
- FindBA. If not possible, explain.
- FindCA. If not possible, explain.
- Find 4BT. If not possible, explain.
- FindA+C. If not possible, explain.
- FindD−A. If not possible, explain.
- Find 2(A+C−D). If not possible, explain.
- Find(A+C)B. If not possible, explain.
- FindB(A+C). If not possible, explain.
- Show thatA(C+D) =AC+AD.
- Show thatA(C−D) =AC−AD.
Practice using your calculator for #12-#15.
E=
312 59 34
342 156 189
783 23 133
,F=
33 72 21
93 41 94
62 75 72
,G=
11 735 67
93 456 2
94 34 0
- FindE+F+G.
- Find 2E.