8.4. Matrix Algebra http://www.ck12.org
Guided Practice
- Show that a 3×3 identity matrix works as the multiplicative identity.
- Use your calculator to input and compute the following matrix operations.
A=
54 65 12
235 322 167
413 512 123
, B=
163 212 466
91 221 184
42 55 42
AT·B·A− 100 A
- Matrix multiplication can be used as a transformation in the coordinate system. Consider the triangle with
coordinates (0, 0) (1, 2) and (1, 0) the following matrix:
[cos 90◦ sin 90◦
−sin 90 cos 90]
What does the new picture look like?
Answers:
- A 3×3 matrix multiplied by the identity should yield the original matrix.
a b c
d e f
g h i
·
1 0 0
0 1 0
0 0 1
=
a b c
d e f
g h i
a 11 =a· 1 +b· 0 +c· 0 =a
a 12 =a· 0 +b· 1 +c· 0 =b
...- Most graphing calculators like the TI-84 can do operations on matrices. Find where you can enter matrices and
enter the two matrices.