Download Multiplicative Inverses of Matrices and Matrix Equations 1. Find the

7/30/2014
Multiplicative Inverses of
Matrices and Matrix Equations
1. Find the products AB and BA to
determine whether B is a
multiplicative inverse of A
2 − 3
7 − 1
A=
B=


1 4 
5 9 
3. Use the following fact:
2. Find the products AB and BA to
determine whether B is a
multiplicative inverse of A
4 
3
 7 − 4
13
13
A=
B=

7
2


− 2 3 
 13 13
5. Find A-1 by forming [A|I] and
then using row operations to
obtain [I|B] where A-1 = [B]. Check
that AA-1 = I and A-1A = I
3 − 1
A=

4 5 
a b 
1  d − b
A=
, then A−1 =

ad − bc − c a 
c d 
to find the inverse of each matrix, if possible.
Check that the matrix you find is the inverse.
 3 − 2
A=

4 1 
6. Write each linear system as a
matrix equation in the form AX = B
where A is the coefficient matrix
and B is the constant matrix
3 x + 7 y = 10
4x − 2 y = 9
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8. Write each matrix equation as a
system of linear equations without
matrices
2 − 3  x   − 1 
 4 5   y  = − 7 

   
9. a) Write each linear system as a
matrix equation in the form AX = B.
b) Solve the system using the inverse
that is given for the coefficient matrix.
3 x − 5 y + z = −1
x − 3 y − 2z = 3
4 x + y + 3z = 3
the inverse of
16
13 
−7
3 − 5 1 
47
47
47 
1 − 3 − 2 is  − 11
5
7



47 
 13 47 − 2347
4 1
−4 
3 
 47
47
47 
2