The matrix A2 + 4A - 5I, where I is identity matrix and A = [1&2 4&-3] , equals

Question

The matrix A2 + 4A - 5I, where I is identity matrix and A = [1&2 4&-3] , equals (A) 4[2&1 2&0] (B) 4[0&-1 2&2] (C) 32[2&1 2&0] (D) 32[1&1 1&0]

Tardigrade Admin · Accepted Answer

A2 + 4A - 5I = A × A + 4A - 5I = [1&2 4&-3] ×[1&2 4&-3] + 4 [1&2 4&-3] -5 [1&0 0&1] = [9&-4 -8&17]+[4&8 16&-12] - [5&0 0&5] = [9+4-5&-4+8-0 -8+16-0&17-12-5] = [8&4 8&0] = 4 [2&1 2&0]

Q. The matrix $A^{2} + 4 A - 5 I$ , where I is identity matrix and $A = [14 2 - 3]$ , equals

$4 [2210]$

$4 [02 - 1 2]$

$32 [2210]$

$32 [1110]$

$A^{2} + 4 A - 5 I = A \times A + 4 A - 5 I$
$= [14 2 - 3] \times [14 2 - 3] + 4 [14 2 - 3] - 5 [1001]$
$= [9 - 8 - 4 17] + [416 8 - 12] - [5005]$
$= [9 + 4 - 5 - 8 + 16 - 0 - 4 + 8 - 0 17 - 12 - 5] = [8840]$
$= 4 [2210]$

Q. The matrix A2+4A−5I, where I is identity matrix and A=[14​2−3​], equals

4[22​10​]

4[02​−12​]

32[22​10​]

32[11​10​]