1. (a) Test whether the following matrix is idempotent, involutory or not. -1 [4 P = 3 [3 -4] -4 -1 -3. 1 21 (b) If A = |2 -1 3 then find the value of A3 – 2A² + A – 1. 11 3.

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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solvw these matrix problem in a easy method

Test whether the following matrix is idempotent, involutory or not.
[4
P = 3
[3
1.
(a)
-1
-4
-4
-1
-3
[1
If A = |2
3
21
(b)
3 then find the value of A3 – 2A² + A – I.
-1
1.
2.
(a) Consider the matrices
3
01
6.
1
31
4
, C = |-1
A =
B =
1
[3 1
1
1.
4
1
3.
Compute Trace (B" A" + 2C") (if possible)
(b) Using inverse matrix solve the following system of linear equations:
3x1 + x2 + X3
+ 2x3 = 0
5x1 + х2 + 2xз
= 1
2х1
= 2
Transcribed Image Text:Test whether the following matrix is idempotent, involutory or not. [4 P = 3 [3 1. (a) -1 -4 -4 -1 -3 [1 If A = |2 3 21 (b) 3 then find the value of A3 – 2A² + A – I. -1 1. 2. (a) Consider the matrices 3 01 6. 1 31 4 , C = |-1 A = B = 1 [3 1 1 1. 4 1 3. Compute Trace (B" A" + 2C") (if possible) (b) Using inverse matrix solve the following system of linear equations: 3x1 + x2 + X3 + 2x3 = 0 5x1 + х2 + 2xз = 1 2х1 = 2
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