http://www.ck12.org Chapter 8. Systems and Matrices
A=
1 2 3
1 0 1
0 2 − 1
,A−^1 =
− 113 43 13
61 −^1613
3 −^13 −^13
- Use a calculator to computeA−^1 , computeA−^1 ·A, computeA·A−^1 and computeA−^1 ·
96
36
− 12
.
- The identity matrix happens to be its own inverse. Find another matrix that is its own inverse.
Answers:
A−^1 ·A=
−^134313
(^16) − (^1613)
(^13) − (^13) − (^13)
·
1 2 3
1 0 1
0 2 − 1
=
a 11 =−^13 · 1 +^43 · 1 +^13 · 0 = 1
a 22 =^16 · 2 −^16 · 0 +^13 · 2 = 1
a 33 =^13 · 3 −^13 · 1 −^13 (− 1 ) = 1Note that the rest of the entries turn out to be zero. This is left for you to confirm.
- Start by entering just matrixAinto the calculator.
To compute matrixA−^1 use the inverse button programmed into the calculator. Do not try to raise the matrix to the
negative one exponent. This will not work.
Note that the calculator may return decimal versions of the fractions and will not show the entire matrix on its limited
display. You will have to scroll to the right to confirm thatA−^1 matches what you have already found. Once you
have foundA−^1 go ahead and store it as matrixBso you do not need to type in the entries.