Home
Class 12
MATHS
If A=[[3, 1],[-1, 2]], show that A^2-5A+...

If `A=[[3, 1],[-1, 2]]`, show that `A^2-5A+7I=0`

Text Solution

AI Generated Solution

To show that \( A^2 - 5A + 7I = 0 \) for the matrix \( A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} \), we will follow these steps: ### Step 1: Calculate \( A^2 \) To find \( A^2 \), we multiply matrix \( A \) by itself: \[ A^2 = A \cdot A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} \cdot \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} \] ...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A= [[3,1] , [-1,2]] then show that A^2 - 5A+7I =0 Hence find A^(-1)

If A=[[4, -1], [-1, k]] such that A^(2)-6A+7I=0 and k=

If A=[{:(3,1),(-1,2):}] , show that A^(2)-5A+7I=O . Hence, find A^(-1) .

If A=[[3, 1], [-1, 2]] and A^(2)-5A+7I=0 , then I=

If A=[31-12], show that A^(2)-5A+7I_(2)=O

If =[31-12], show that A^(2)-5A+7I_(2)=O

If A=[3112], show that A^(2)-5A+7I=0 Hence find A^(-1) .

If A=[31-12], show that A^(2)-5A+7I=O. Hence,find A^(-1)

If A=[[3,2,01,4,00,0,5]], show that A^(2)-7A+10I_(3)=O

If A=[(5,3),(12,7)] , show that A^(2)-12A-I=0 . Hence find A^(-1) .