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If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] an...

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

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To solve the problem, we need to show that \( A^2 - 5A + 7I = 0 \) and then find the inverse of matrix \( A \). ### Step 1: Calculate \( A^2 \) Given: \[ A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} \] ...
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If A=[[3, 1],[-1, 2]] , show that A^2-5A+7I=0

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

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

If A=[(2,-3),(3,4)], show the A^2-6A+17I=0. Hence find A^-1

If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then show that A^2=B^2=C^2=I_2 .

If A=[[1,2,3],[0,1,0],[1,1,0]] and B=[[-1,1,0],[0,-1,1],[2,3,4]] show that AB!=BA

If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so that A^2=5A+lambdaI

If A A=[[3,-2],[ 4,-2]] and I=[[1, 0],[ 0, 1]] , find k so that A^2=k A-2I .

If A= [[1 , 0],[ − 1, 7]] and I=[[1, 0],[ 0 ,1]] , then find k so that A^2=8A+k I

If A=[[0,1],[1,0]],B=[[0,-i],[i,0]] and C=[[i,0],[0,-i]] , show that A^2=B^2=-C^2=I_2 and AB=-BA,AC=-CA and BC=-CB .

NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Exercise 4.5
  1. Find the adjoint of each of the matrices [{:(1,2),(3,4):}]

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  2. Find adjoint of the matrice in[1-1 2 2 3 5-2 0 1]

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  3. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

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  4. Verify A" "(a d j" "A)" "=" "(a d j" "A)" "A" "=" "|A|"I" |1-1 2 3 0-...

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  5. Find the inverse the matrix (if it exists)given in[2-2 4 3]

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  6. Find the inverse the matrix (if it exists)given in[-1 5-3 2]

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  7. Find the inverse the matrix (if it exists)given in[1 2 3 0 2 4 0 0 5]

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  8. Find the inverse the matrix (if it exists)given in [1 0 0 3 3 0 5 2-1]

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  9. Find the inverse the matrix (if it exists) given in[2 1 3 4-1 0-7 2 1]

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  10. Find the inverse the matrix (if it exists)given in[1-1 2 0 2-3 3-2 4]

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  11. Find the inverse the matrix (if it exists)given in[0 0 0 0cosalphasina...

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  12. If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=...

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  13. If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]], show that A...

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  14. Solve system of linear equations, using matrix method, x- y" "+" "2...

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  15. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

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  16. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

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  17. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

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  18. If A is an invertible matrix, then det(A^(-1)) is equal to det(A) (...

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