Matrices and Determinants Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. If aij =\({1\over2}(3i-2j)\) and A=[aij]2x2 is

    (a)

    \(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)

    (b)

    \(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)

    (c)

    \(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)

    (d)

    \(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)

  2. What must be the matrix X, if 2x+\(\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?\)

    (a)

    \(\begin{bmatrix} 1& 3 \\ 2 &-1 \end{bmatrix}\)

    (b)

    \(\begin{bmatrix} 1& -3 \\ 2 &-1 \end{bmatrix}\)

    (c)

    \(\begin{bmatrix} 2& 6 \\ 4 &-2 \end{bmatrix}\)

    (d)

    \(\begin{bmatrix} 2& -6 \\ 4 &-2 \end{bmatrix}\)

  3. If A is a square matrix, then which of the following is not symmetric?

    (a)

    A+ AT

    (b)

    AAT

    (c)

    AT A

    (d)

    A− AT

  4. If A=\(\begin{bmatrix}a & x \\ y& a \end{bmatrix}\) and if xy =1, then det(A AT ) is equal to

    (a)

    (a −1)2

    (b)

    (a2 +1)2

    (c)

    a2 −1

    (d)

    (a2 −1)2

  5. If the points (x,−2), (5, 2), (8,8) are collinear, then x is equal to

    (a)

    -3

    (b)

    \({1\over 3}\)

    (c)

    1

    (d)

    3

  6. 3 x 2 = 6
  7. Determine 3B + 4C - D if B, C, and D are given by
    B= \(\begin{bmatrix} 2 & 3 & 0\\1 & -1 & 5\end{bmatrix}\) ,C=\(\begin{bmatrix} -1 & -2 & 3\\-1 & 0 & 2\end{bmatrix}\),D= \(\begin{bmatrix} 0 & 4 & -1\\5 & 6 & -5\end{bmatrix}\)

  8. Determine the matrices A and B if they satisfy 
    \(2A-B+\begin{bmatrix} 6 & -6 & 0\\ -4 & 2 & 1\end{bmatrix}=0 \ and \ A-2B=\begin{bmatrix} 3 & 2&8 \\ -2 & 1&-7 \end{bmatrix}\)

  9. Find |A| if A=\(\begin{bmatrix} 0& sin \alpha &cos \alpha \\ sin \alpha & 0 & sin \beta \\ cos \alpha & -sin\beta & 0 \end{bmatrix}\) .

  10. 3 x 3 = 9
  11. 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(AB)T=BTAT

  12. If =\(\begin{bmatrix} 1 &0 &0 \\0 & 1 & 0 \\a &b &-1 \end{bmatrix}\) , show that A2 is a unit matrix.

  13. 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 (A+B)T=AT+BT=BT+AT

  14. 2 x 5 = 10
  15. For what value of x, the matrix A=\(\begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & x^3 \\ 2 & -3 & 0 \end{bmatrix}\) is skew-symmetric

  16. A shopkeeper in a Nuts and Spices shop makes gift packs of cashew nuts, raisins, and almonds.
    Pack I contains 100 gm of cashew nuts, 100 gm of raisins and 50 gm of almonds.
    Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds.
    Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds.
    The cost of 50 gm of cashew nuts is Rs.50, 50 gm of raisins is Rs.10, and 50 gm of almonds is Rs.60. What is the cost of each gift pack?

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