Advertisements
Advertisements
प्रश्न
If `A=([2,0,1],[2,1,3],[1,-1,0])` find A2 - 5A + 4I and hence find a matrix X such that A2 - 5A + 4I + X = 0
उत्तर
`A=[[2,0,1],[2,1,3],[1,-1,0]]`
`A^2=A A=[[2,0,1],[2,1,3],[1,-1,0]][[2,0,1],[2,1,3],[1,-1,0]]=[[5,-1,2],[9,-2,5],[0,-1,-2]]`
Also,`-5A=[[-10,0,-5],[-10,-5,-15],[-5,5,0]]`
`A^2-5A+4I=[[5,-1,2],[9,-2,5],[0,-1,-2]]-[[-10,0,-5],[-10,-5,-15],[-5,5,0]]+[[4,0,0],[0,4,0],[0,0,4]]=[[-1,-1,-3],[-1,-3,-10],[-5,4,2]]`
Now
`A^2-5A+4I+X=O`
`=>X=-(A^2-5A+4I)`
`=>X=(-1)[[-1,-1,-3],[-1,-3,-10],[-5,4,2]]=[[1,1,3],[1,3,10],[5,-4,-2]]`
APPEARS IN
संबंधित प्रश्न
If A = `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where AT is transpose of A.
If `A=[[1,2,2],[2,1,2],[2,2,1]]` ,then show that `A^2-4A-5I=0` and hence find A-1.
Compute the following:
`[(a^2+b^2, b^2+c^2),(a^2+c^2, a^2+b^2)] + [(2ab , 2bc),(-2ac, -2ab)]`
If F(x) = `[(cosx, -sinx,0), (sinx, cosx, 0),(0,0,1)]` show that F(x)F(y) = F(x + y)
Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: B − 4C
Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 3A − C
If A =`[[2,3],[5,7]],B =` `[[-1,0 ,2],[3,4,1]]`,`C= [[-1,2,3],[2,1,0]]`find : A + B and B + C
If A =`[[2 3],[5 7]],B =` `[[-1 0 2],[3 4 1]]`,`C= [[-1 2 3],[2 1 0]]`find
2B + 3A and 3C − 4B
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find
2A + 3B − 5C
Find matrices X and Y, if X + Y =`[[5 2],[0 9]]`
and X − Y = `[[3 6],[0 -1]]`
f X − Y =`[[1 1 1],[1 1 0],[1 0 0]]` and X + Y = `[[3 5 1],[-1 1 1],[11 8 0]]`find X and Y.
If A = `[[1 -3 2],[2 0 2]]`and `B = [[2 -1 -1],[1 0 -1]]` find the matrix C such that A + B + C is
, find the matrix C such that A + B + C is zero matrix.
Find x, y, z and t, if
`2[[x 5],[z t]]+[[x 6],[-1 2t]]=[[7 14],[15 14]]`
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
`2X + 3Y = [[2,3],[4,0]], 3X+2Y = [[-2,2],[1,-5]]`
If \[A = \begin{bmatrix}\cos x & \sin x \\ - \sin x & \cos x\end{bmatrix}\] , find x satisfying 0 < x < \[\frac{\pi}{2}\] when A + AT = I
If \[\begin{bmatrix}xy & 4 \\ z + 6 & x + y\end{bmatrix} = \begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}\] , write the value of (x + y + z).
If possible, find the sum of the matrices A and B, where A = `[(sqrt(3), 1),(2, 3)]`, and B = `[(x, y, z),(a, "b", 6)]`
If A = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: A(B + C) = AB + AC
If A = `[(1, 0, -1),(2, 1, 3 ),(0, 1, 1)]`, then verify that A2 + A = A(A + I), where I is 3 × 3 unit matrix.
If A = `[(0, -x),(x, 0)]`, B = `[(0, 1),(1, 0)]` and x2 = –1, then show that (A + B)2 = A2 + B2.
If A `= [(0,2),(2,0)],` then A2 is ____________.
If a2 + b2 + c2 = –2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, (1 + c^2)x)|` then f(x) is a polynomial of degree ______.
Let A = `[(1, -1),(2, α)]` and B = `[(β, 1),(1, 0)]`, α, β ∈ R. Let α1 be the value of α which satisfies (A + B)2 = `A^2 + [(2, 2),(2, 2)]` and α2 be the value of α which satisfies (A + B)2 = B2 . Then |α1 – α2| is equal to ______.
