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Construct a 3 xx2matrix whose elements a...

Construct a `3 xx2`matrix whose elements are given by `a_(i j)=1/2|i-3j|`.

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To construct a \(3 \times 2\) matrix whose elements are given by \(a_{ij} = \frac{1}{2}|i - 3j|\), we will follow these steps: ### Step 1: Define the matrix structure We need to create a matrix \(A\) with 3 rows and 2 columns. The elements of the matrix will be denoted as follows: \[ A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ ...
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NCERT ENGLISH-MATRICES-All Questions
  1. Consider the following information regarding the number of men and wo...

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  2. If a matrix has 8 elements, what are the possible orders it can have?

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  3. Construct a 3 xx2matrix whose elements are given by a(i j)=1/2|i-3j|.

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  4. Find 1/2(A+Aprime)and 1/2(A-Aprime), when A=[[0,a, b],[-a,0,c],[-b,-c,...

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  5. For the matrix A=[[1, 5],[ 6, 7]], verify that.(i) (A+A^(prime))is a ...

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  6. For the matrices A and B, verify that (AB)′=B′A′, where (i) A=[{:(-1)...

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  7. If Aprime=[[-2, 3],[ 1, 2]]and B=[[-1, 0],[ 1, 2]], then find (A+2B)^(...

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  8. (i) Show that the matrix A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]]is a symm...

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

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

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

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

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

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

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

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

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

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

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

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