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Find the transpose of each of the following matrices:(i) `[[5],[ 1/2],[-1]]` (ii) `[[1,-1],[ 2, 3]]` (iii) `[[-1, 5, 6],[sqrt(3),5, 6],[ 2 ,3,-1]]`

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To find the transpose of the given matrices, we will follow the rule that states: the transpose of a matrix is obtained by swapping its rows with its columns. ### Step-by-Step Solution: **(i)** For the matrix \( A = \begin{bmatrix} 5 \\ \frac{1}{2} \\ -1 \end{bmatrix} \): 1. Identify the elements of the matrix: - First row: \( 5 \) ...
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NCERT ENGLISH-MATRICES-All Questions
  1. (i) Show that the matrix A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]]is a symm...

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  2. If (i) A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]], then verify that ...

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  3. Find the transpose of each of the following matrices:(i) [[5],[ 1/2],...

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  4. If A=[[3,4],[ -1,2],[0, 1]]and B=[[-1, 2, 1],[1,2, 3]], then verify th...

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  5. If A=[[-1 ,2, 3],[ 5 ,7, 9],[-2 ,1, 1]]and B=[[-4, 1,-5],[ 1, 2,0 ],[1...

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  6. If A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]], then A+A^(prime)=I, i...

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  7. Express the following matrices as the sum of a symmetric and a skew s...

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  8. Choose the correct answer If A, B are symmetric matrices of same orde...

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  9. Find A^2-5A+6I, if A=[[2, 0, 1],[ 2, 1, 3],[ 1,-1, 0]]

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  10. Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1]...

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  11. If A A=[[3,-2],[ 4,-2]]and I=[[1, 0],[ 0, 1]], find k so that A^2=k A-...

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  12. If A=[[1, 0 ,2 ],[0 ,2 ,1],[2, 0 ,3]], prove that A^3-6A^2+7A+2I=0

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  13. If x[[2] ,[3]]+y[[-1] ,[1]]=[[10] ,[5]], find the values of x and y.

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  14. Solve the equation for x, y, z and t, if 2[[x ,z ],[y ,t]]+3[[1,-1 ],[...

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  15. If F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[ 0, 0, 1]], show that F(x) F(y)...

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  16. Given 3[[x, y],[ z, w]]=[[x,6],[-1, 2w]]+[[4,x+y],[ z+w,3]], find the ...

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  17. A trust fund has Rs 30,000 that must be invested in two different typ...

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  18. If A=[ [0,-tan((alpha)/2)],[tan(alpha/2),0]] then (I-A)[[cosalpha,-...

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  19. Using elementary transformations, find the inverse of the matrix[[2,-...

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  20. Using elementary transformations, find the inverse of the matrix[[6,-...

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