Your cart is empty.
Practice each question, then open the answer or worked solution.
Show that satisfies the equation A2 – 3A – 7I = 0 and hence find A-1.
Given,
Now,
A2 – 3A – 7I = 0
Multiplying both sides with A-1, we get
A-1 [A2 – 3A – 7I] = A-1 0
A-1. A . A – 3A-1. A – 7A-1. I = 0
I . A – 3I – 7A-1 = 0 [As A-1. A = I]
A – 3I – 7A-1 = 0
7A-1 = A – 3I
Find the matrix A satisfying the matrix equation:
Now,
P-1 PAQ = P-1 I
So, IAQ = P-1
AQ = P-1
AQQ-1 = P-1 Q-1
AI = P-1 Q-1
A = P-1 Q-1
Find A, if
On comparing elements of both sides, we have
4x = -4 ⇒x = -1
4y = 8 ⇒ y = 2
And, 4z = 4 ⇒ z = 1
Therefore, A = [-1 2 1]
If then verify
(BA)2 ≠ B2 A2
The given matrices A has order 3 x 2 and B has order 2 x 3.
So, BA is defined and will have order 3 x 3.
But, A2 and B2 are not defined as the orders don’t satisfy the multiplication condition.
Hence, (BA)2 ≠ B2 A2
If possible, find BA and AB where
Show by an example that for A ≠ 0, B ≠ 0, AB = 0.
– Hence Proved
Given Is (AB)’ = B’ A’ ?
From (i) and (ii), we have
(AB)’ = B’ A’
Solve for x and y:
Now, we have
2x + 3y – 8 = 0 ….. (1) and
x + 5y – 11 = 0 ….. (2)
On solving the equations (1) and (2), we get
x = 1 and y = 2
If X and Y are 2 x 2 matrices, then solve the following matrix equations for X and Y
If A = [3 5], B = [7 3], then find a non-zero matrix C such that AB = AC.
Given, A = [3 5]1×2 and B = [7 3]1×2
For AC = BC
We have order of C = 2 x n
