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If A = [[3,-5],[-4,2]],show that A^2-5A-...

If A = `[[3,-5],[-4,2]]`,show that `A^2`-5A-14I =0.

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A = [[3,-5],[-4,2]] , verify that A^2 -5A-14I=0, hence find A^(-1)

If A = [[4,5],[5,6]] , show that A^2 = 10A + I where I is the unit matrix of order 2.

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

If A = ([1,4],[2,3]) then show that A^2-4A-5I = theta and using this find A^(-1) . Where I= ([1,0],[0,1]) and theta = ([0,0],[0,0]) .

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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If A = [(3,-5),(-4,2)] then show that A+A' is a symmetric matrix.

If A={:[(3,-5),(-4,2)], find A^(2)-5A-14I.

If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that (AB)^T=B^TA^T were A^T is the transpose of A.

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

PATHFINDER-MATRICES-QUESTION BANK
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  2. Find the values of x,y,z if , [[2x+y,x-y],[x-z,x+y+z]]=[[10,-1],[2,8]]

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  3. If A=[[2,-2],[4,2],[-5,1]]B=[[8,0],[4,-2],[3,6]]find the martrix X,suc...

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  4. Solve the matrix equation , [(x^2),(y^2)]-3 [(x),(2y)]=[(-2),(9)]

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  5. Assume that y, w and are matrices of order 3xxk,nxx3 and pxxk respecti...

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  6. If A is a squre matrix such that A^2 =A, then find the value of (1+A)^...

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  7. Find the inveres of [[1,2,4],[3,-19,7],[2,4,8]], if exists.

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  8. A and B are non-singular matrices of same order then show that adj(AB)...

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  9. If A = [[3,-5],[-4,2]],show that A^2-5A-14I =0.

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  10. If A =[[costheta,sintheta],[-sintheta,costheta]] then prove that A^n=[...

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  11. If A = [1,3,4],B=[[2,1],[3,7],[6,8]], C=[[3,4],[5,6],[1,0]] verify tha...

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  12. Express [[4,3,7],[6,5,-8],[1,2,6]] as the sum of a symmetric matrix an...

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  14. Let A = [[0,-tanalpha//2],[tanalpha//2,0]] and I, the indentity matrix...

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  15. Show that I+A =(I+A)*I

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  16. If A=[[2,-2],[4,2],[-5,1]]B=[[8,0],[4,-2],[3,6]]find the martrix X,suc...

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  17. If A=[[1,2],[-4,2]], then verify that A (adjA)=(adjA)A =abs(A)I2

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  18. A = [[3,-5],[-4,2]], verify that A^2-5A-14I=0, hence find A^(-1)

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  19. Find A^(-1) if A = [1,2,-3][2,3,2] [3,-3,-4] Hence solve the equations...

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  20. Obtain the inverse of the following matrix using elementary operations...

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