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If A=[[-2],[4], [5]], B=[[1 ,3,-6]], ver...

If `A=[[-2],[4], [5]]`, `B=[[1 ,3,-6]]`, verify that `(A B)' = B'A'`.

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To verify that \((AB)' = B'A'\) for the given matrices \(A\) and \(B\), we will follow these steps: ### Step 1: Define the matrices Given: \[ A = \begin{bmatrix} -2 \\ 4 \\ 5 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 & -6 \end{bmatrix} \] ...
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NCERT ENGLISH-MATRICES-All Questions
  1. By using elementary operations, find the inverse of the matrix A=[[1,...

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  2. If A=[3sqrt(3)2 4 20]and B=[2-1 2 124], verify that(i) (Aprime)prime=A...

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  3. If A=[[-2],[4], [5]], B=[[1 ,3,-6]], verify that (A B)' = B'A'.

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  4. Let A=[[2,-1],[3,4]],B=[[5,4],[7,4]],C=[[2,5],[3,8]]. Find a matrix D ...

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  5. The number of all possible matrices of order 3 xx3with each entry 0 or...

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  6. Find x, if [x-5-1][[1, 0 ,2 ],[0,2, 1 ],[2 ,0 ,3]][[x],[4] ,[1]]=O.

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

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  8. Show that the matrix B^TA B is symmetric or skew-symmetric according a...

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  9. If A and B are symmetric matrices, prove that AB – BA is a skew symme...

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  10. For what values of x : [[1, 2, 1]][[1 ,2 ,0],[ 2, 0, 1],[ 1, 0, 2]][[0...

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  11. Find the values of x, y, z if the matrix A=[[0, 2y, z],[ x, y,-z],[ x...

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  12. Let A=[[0, 1],[ 0, 0]]show that (a I+b A)^n=a^n I+n a^(n-1)b A, where...

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  13. If A=[[3,-4],[1,-1]], then prove that A^n=[[1+2n,-4n],[n,1-2n]], where...

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  14. If A=[[1, 1, 1],[ 1, 1, 1],[ 1, 1, 1]], prove that A^n=[[3^(n-1),3^(n-...

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  15. The bookshop of a particular school has 10 dozen chemistry books, 8 d...

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  16. Assume X, Y, Z, W and P are matrices of order 2 xxn, 3 xxk, 2 xxp, n ...

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  17. Assume X,Y,Z ,W,P are the matrices of order 2 xx n, 3 xx k,2 xx p, n x...

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  18. If A=[[1,-2, 3,],[ 4, 2, 5,]]and B=[[2, 4], [2,3],[ 5, 1]], then find ...

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  19. Find AB, if A=[[6, 9],[ 2, 3]]and B=[[2 ,6, 0],[ 7, 9, 8]].

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  20. Two farmers Ramkishan and Gurcharan Singh cultivates only three var...

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