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If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0...

If `[2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A` , then write the order of matrix `A` .

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To find the order of the matrix \( A \) given by the multiplication of three matrices, we will follow these steps: ### Step 1: Identify the matrices and their orders 1. The first matrix \( X \) is given as: \[ X = \begin{bmatrix} 2 & 1 & 3 \end{bmatrix} \] This is a \( 1 \times 3 \) matrix (1 row and 3 columns). ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find the value...

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  2. Write the number of all possible matrices of order 2xx2 with each e...

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  3. If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order o...

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  4. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

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  5. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

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  6. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

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  7. If A and B are two matrices such that A B=A and B A=B , then B^...

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  8. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

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  9. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

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  10. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

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  11. If the matrix A B is zero, then It is not necessary that either A=O...

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  12. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

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  13. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

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  14. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

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  15. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0,...

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  16. If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 0 0 1] and A B=I3 , then x+y e...

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  17. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

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  18. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

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  19. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

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  20. If a square matrix such that A^2=A , then (I+A)^3-7A is equal to A ...

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