Matrices Test

Matrices

This is Matrices Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If A + B = \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 1&1 \end{array}} \right]\) and A – 2 B =\(\left[ {\begin{array}{*{20}{c}} { - 1}&1 \\ 1&{ - 1} \end{array}} \right]\), then A =
  • A
    none of these.
  • B
    \(\left[ {\begin{array}{*{20}{c}} 1&1 \\ 2&1 \end{array}} \right]\)
  • C
    \(\frac{1}{3}\left[ {\begin{array}{*{20}{c}} 1&1 \\ 2&1 \end{array}} \right]\)
    Correct
  • D
    \(\frac{1}{3}\left[ {\begin{array}{*{20}{c}} 2&1 \\ 1&2 \end{array}} \right]\)
2
The order of the single matrix obtained fromis \({\left[ {\begin{array}{*{20}{c}} 1&{ - 1} \\ 0&2 \\ 2&3 \end{array}} \right]_{3 \times 2}}\left\{ {{{\left[ {\begin{array}{*{20}{c}} { - 1}&0&2 \\ 2&0&1 \end{array}} \right]}_{2 \times 3}} - {{\left[ {\begin{array}{*{20}{c}} 0&1&{23} \\ 1&0&{21} \end{array}} \right]}_{2 \times 3}}} \right\}\)
  • A
    \(2{\text{ }} \times {\text{ }}3\)
  • B
    \(3{\text{ }} \times {\text{ }}2\)
  • C
    \(2{\text{ }} \times {\text{ }}2\)
  • D
    \(3{\text{ }} \times {\text{ }}3\)
    Correct
3
Adj.(KA) = ….
  • A
    \({K^n}Adj.A\)
  • B
    \({K^{n - 1\;}}Adj.A\)
    Correct
  • C
    K Adj. A
  • D
    None of these
4
If A and B are any two square matrices of the same order, then
  • A
    \({(AB)^t} = {A^t}{B^t}\)
  • B
    adj (AB) = adj (A) adj (B)
  • C
    AB = O
  • D
    \({(AB)^t} = {B^t}{A^t}\)
    Correct
5
If A is any square matrix, then
  • A
    none of these.
  • B
    \(A + {A^t}\)is symmetric
    Correct
  • C
    \(A + {A^t}\)is skew-symmetric
  • D
    \(A - {A^t}\)is symmetric
6
If A any square matrix then which of the following is not symmetric ?
  • A
    \(A + {A^t}\)
  • B
    \(A{A^t}\)
  • C
    \({A^t}A\)
  • D
    \(A - {A^t}\)
    Correct
7
Each diagonal element of a skew-symmetric matrix is
  • A
    non-real
  • B
    negative.
  • C
    Positive
  • D
    Zero
    Correct
8
The matrix \(\left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]\) is
  • A
    a skew- symmetric matrix.
  • B
    a symmetric matrix
    Correct
  • C
    a diagonal matrix
  • D
    a unit matrix
9
If \(A = \left[ {\begin{array}{*{20}{c}} 0&2&{ - 3} \\ { - 2}&0&{ - 1} \\ 3&1&0 \end{array}} \right]\)then A is a
  • A
    none of these.
  • B
    symmetric matrix
  • C
    skew-symmetric matrix
    Correct
  • D
    diagonal matrix
10
If \(A = \left[ {\begin{array}{*{20}{c}} 0&2&3 \\ { - 2}&0&{ - 7} \\ { - 3}&7&0 \end{array}} \right]\) , then ,which of the following is true :
  • A
    None of these.
  • B
    A = - A’
    Correct
  • C
    A = - A
  • D
    A = A’
11
If A and B are symmetric matrices of order n ( A\( \ne \) B), then
  • A
    A + B is a diagonal matrix
  • B
    A + B is skew symmetric
  • C
    A + B is a zero matrix.
  • D
    A + B is symmetric
    Correct
12
If\(A = \left[ {\begin{array}{*{20}{c}} 0&{ - 1}&2 \\ 1&0&3 \\ { - 2}&{ - 3}&0 \end{array}} \right]\), \(A + 2{A^t}\) equals
  • A
    A
  • B
    \( - {A^t}\)
  • C
    \(2{A^2}\)
  • D
    \({A^t}\)
    Correct
13
If A is a square matrix, then A – A’ is a
  • A
    none of these.
  • B
    skew-symmetric matrix
    Correct
  • C
    symmetric matrix
  • D
    diagonal matrix
14
If A is square matrix such that \({A^2} = I\), then \({A^{ - 1}}\) is equal to
  • A
    O
  • B
    I
  • C
    A
    Correct
  • D
    A + I.
15
The system of linear equations ax+ b y= 0, cx + dy = 0 has a non-trival solution if
  • A
    ad – bc < 0
  • B
    ad – bc = 0
    Correct
  • C
    ad –bc = 0.
  • D
    ac + bd = 0