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11th Standard English Medium Maths Subject Matrices and Determinants Book Back 2 Mark Questions with Solution Part - I

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 20

    2 Marks

    10 x 2 = 20
  1. Suppose that a matrix has 12 elements. What are the possible orders it can have? What if it has 7 elements?

  2. Find x, y, a, and b if \(\begin{bmatrix} 3x+4y & 6 & x-2y \\ a+b & 2a-b & -3 \end{bmatrix}\)=\(\begin{bmatrix} 2 & 6 & 4 \\ 5 & -5 & -3 \end{bmatrix}\)

  3. Compute A + B and A - B if A =\(\begin{bmatrix} 4 & \sqrt { 5 } & 7 \\ -1 & 0 & 0.5 \end{bmatrix}\) and B = \(\begin{bmatrix} \sqrt { 3 } & \sqrt { 5 } & 7.3 \\ 1 & {1\over3} &{1\over4} \end{bmatrix}\) .

  4. If A =\(\begin{bmatrix} 4 & 6 & 2 \\ 0 & 1 & 5 \\ 0 & 3 & 2 \end{bmatrix}\) and B = \(\begin{bmatrix} 0 & 1 & -1 \\ 3 & -1 & 4 \\ -1 & 2 & 1 \end{bmatrix}\) verify (A - B)= A- BT

  5. If A =\(\begin{bmatrix} 4 & 6 & 2 \\ 0 & 1 & 5 \\ 0 & 3 & 2 \end{bmatrix}\) and B = \(\begin{bmatrix} 0 & 1 & -1 \\ 3 & -1 & 4 \\ -1 & 2 & 1 \end{bmatrix}\)
    verify (3A)= 3AT

  6. Construct an m \(\times\) n matrix A = [aij], where a ij is given by
    \(a_{ij}={(i-2j)^2\over 2}with \ m=2,n=3\)

  7. Determine the value of x + y if \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\)

  8. Give your own examples of matrices satisfying the following conditions in each case:
    (i) A and B such that AB \(\neq\) BA.
    (ii) A and B such that \(A B=O=B A, A \neq O \text {and } B \neq O \text {. }\)
    (iii) A and B such that \(A B=O \text {and } B A \neq O\)

  9. If AT=\(\begin{bmatrix} 4 & 5 \\ -1 & 0 \\ 2 & 3 \end{bmatrix}\) and B =  \(\begin{bmatrix} 2 & -1&1 \\7 & 5&-2 \end{bmatrix}\), verify (BT)= B

  10. Evaluate :\(\begin{vmatrix} cos \theta & sin \theta \\ -sin \theta & cos \theta \end{vmatrix}\)

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