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Statement 1: if D=diag[d1, d2, ,dn],the...

Statement 1: if `D=`diag`[d_1, d_2, ,d_n]`,then `D^(-1)=`diag`[d_1^(-1),d_2^(-1),...,d_n^(-1)]` Statement 2: if `D=`diag`[d_1, d_2, ,d_n]`,then `D^n=`diag`[d_1^n,d_2^n,...,d_n^n]`

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CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A=[[-1, 1],[ 0,-2]] , then prove that A^2+3A+2I=Odot Hence, find ...

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  2. If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , ...

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  3. Statement 1: if D=diag[d1, d2, ,dn],then D^(-1)=diag[d1^(-1),d2^(-1),...

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  4. If S is a real skew-symmetric matrix, then prove that I-S is non-si...

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  5. If B and C are non-singular matrices and O is null matrix, then show t...

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  6. Find the possible square roots of the two rowed unit matrix I.

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  7. If A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & 2\\ 2 & 2 & 1 \end{bmatrix} ,...

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  8. Let M be a 3xx3 matrix satisfying M[[0], [1] ,[0]]=[[-1], [2], [3]]...

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  9. If A is unimodular, then which of the following is unimodular? a. -A ...

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  10. Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4)...

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  11. If A B=Aa n dB A=B , then which of the following is/are true? A is ide...

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  12. If A=[[1,-1],[ 2, 1]],B=[[a,1],[b,-1]]a n d(A+B)^2=A^2+B^2+2A B ,t h e...

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  13. Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the t...

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  14. If A=1/3|[1, 2, 2], [2, 1,-2],[a,2,b]| is an orthogonal matrix, then ...

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  15. If A is a matrix such that A^2+A+2I=Odot, the which of the following i...

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  16. If A(theta)=[[sintheta, icostheta], [icostheta, sintheta]] , then whic...

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  17. If |(1,-t a ntheta),(t a ntheta,1)| |(1,t a ntheta),(-t a ntheta,1)|^-...

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  18. If A=[[3,-3, 4], [2,-3, 4], [0,-1, 1]] , then a. a d j(a d j A)=A b. |...

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  19. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

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  20. If A=[a("ij")](4xx4), such that a("ij")={(2",","when "i=j),(0",","when...

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