Identity What number is the multiplication identity for real numbers? For matrices, n x n--square...
-
Upload
lydia-shields -
Category
Documents
-
view
215 -
download
0
Transcript of Identity What number is the multiplication identity for real numbers? For matrices, n x n--square...
![Page 1: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/1.jpg)
4.4 Identity & Inverse Matrices
![Page 2: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/2.jpg)
IdentityWhat number is the multiplication identity for
real numbers?For matrices, n x n--square matrices, has 1’s
on main diagonal and zeros elsewhere2 x 2 3 x 3
1 0
0 1
1 0 0
0 1 0
0 0 1
![Page 3: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/3.jpg)
InverseWhen multiply 2 matrices, A & B, in both
orders, you get the identity matrixAB = IBA = I2 x 2
A a b
c d
1 1A , det 0
A
d b
c a
![Page 4: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/4.jpg)
EXAMPLESFind the inverse of the given matrices1) 2)
3 2
2 4
6 1
8 2
![Page 5: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/5.jpg)
Solving Matrix EquationsFind the inverse of the matrix that is being
multiplied by XMultiply both sides of the equation by that
inverseMake sure to always write the inverse matrix
1st (on left side)
1 1
1
AX B
A AX A B
X A B
![Page 6: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/6.jpg)
EXAMPLESSolve the matrix equation1) 2)3 4 3 8
5 7 2 2X
1 2 7 2
4 7 1 9X
![Page 7: Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ecd5503460f94bda502/html5/thumbnails/7.jpg)
Inverses of 3 x 3Use a graphing calculatorEnter MatrixChoose matrixUse key and press enter
HW: p227-228 #14-36 even, 37-39
1x
0 1 1
2 0 1
1 3 3
A
1 2 3
3 1 2
3 1 1
B