Q. 255.0( 2 Votes )
Show that the matrix, 
satisfies the equation, A3 – A2 – 3A – I3 = O. Hence, find A–1.
Answer :
A = 
A3 = A2.A
A2 = 
= 
A2.A = 
= 
= 
Now, A3 – A2 – 3A – I
= 
= 
= 
Thus, A3 – A2 – 3A – I
Now, (AAA) A – 1. – (A.A) A – 1 – 3.A A – 1 – I.A – 1 = 0
AA(A – 1A) – A(A – 1A) – 3(A – 1A) = – 1(A – 1I)
A2 – A – 3A – I = 0
= A – 1 = 
Now,
= 
= 
= 
Hence, A – 1 = 
Rate this question :
Solve the following systems of homogeneous linear equations by matrix method:
x + y – 6z = 0
x – y + 2z = 0
– 3x + y + 2z = 0
RD Sharma - Volume 1Find the matrix X for which: 
.
Solve the following systems of homogeneous linear equations by matrix method:
x + y + z = 0
x – y – 5z = 0
x + 2y + 4z = 0
RD Sharma - Volume 1Find the matrix X satisfying the equation: 
.
Solve the following systems of homogeneous linear equations by matrix method:
2x + 3y – z = 0
x – y – 2z = 0
3x + y + 3z = 0
RD Sharma - Volume 1Solve the following systems of homogeneous linear equations by matrix method:
3x + y – 2z = 0
x + y + z = 0
x – 2y + z = 0
RD Sharma - Volume 1Find the matrix X satisfying the matrix equation: 
.
If 
, show that A – 1 = A3.
If 
. Verify that A3 – 6A2 + 9A – 4I = O and hence fid A – 1.
