CBSE Questions for Class 12 Commerce Maths Matrices Quiz 1 - MCQExams.com

Let $$X$$ and $$Y$$ be two arbitrary, $$3\times 3$$, non-zero, skew-symmetric matrices and $$Z$$ be an arbitrary $$3\times 3$$, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
  • $$Y^3Z^4-Z^4Y^3$$
  • $$X^{44}+Y^{44}$$
  • $$X^4Z^3-Z^3X^4$$
  • $$X^{23}+Y^{23}$$
If $$\displaystyle A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \end{matrix} \right] $$ and $$\displaystyle I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] $$, then the correct statement is:
  • $$\displaystyle { A }^{ 2 }+5A-7I=O$$
  • $$\displaystyle -{ A }^{ 2 }+5A+7I=O$$
  • $$\displaystyle { A }^{ 2 }-5A+7I=O$$
  • $$\displaystyle { A }^{ 2 }+5A+7I=O$$
If AB = AC then 
  • B = C
  • $$B\neq C$$
  • B need not be equal to C
  • B = -C
If $$\mathrm{A}^{2}=\mathrm{A},\ \mathrm{B}^{2}=\mathrm{B},\ \mathrm{A}\mathrm{B}=\mathrm{B}\mathrm{A}=O$$ (Null Matrix), then $$(\mathrm{A}+\mathrm{B})^{2}=$$
  • $$\mathrm{A}-\mathrm{B}$$
  • $$\mathrm{A}+\mathrm{B}$$
  • $$\mathrm{A}^{2}-\mathrm{B}^{2}$$
  • $$0$$
$$I$$ $$A=\left[\begin{array}{ll}
0 & 1\\ 1 & 0 \end{array}\right]$$,  $$A^{4}=$$
($$I$$ is an identity matrix.)
  • $$I$$
  • $$0$$
  • $$\mathrm{A}$$
  • $$4{I}$$
lf $$\mathrm{A}= \left[\begin{array}{lll}
o & c & -b\\
-c & o & a\\
b & -a & o
\end{array}\right]\mathrm{a}\mathrm{n}\mathrm{d}$$ $$ \mathrm{B}=\left[\begin{array}{lll}
a^{2} & ab & ac\\
ab & b^{2} & bc\\
ac & bc & c^{2}
\end{array}\right],$$ then $$\mathrm{A}\mathrm{B}=$$
  • $$\mathrm{A}$$
  • $$\mathrm{B}$$
  • $$I$$
  • $$\mathrm{O}$$
lIf $$\mathrm{A} =\left[\begin{array}{ll}
a & 0\\
a & 0
\end{array}\right],\ \mathrm{B}=\left[\begin{array}{ll}
0 & 0\\
b & b
\end{array}\right],$$ then $$\mathrm{A}\mathrm{B}=$$ 
  • $$O$$
  • $$\mathrm{B}\mathrm{A}$$
  • $$\mathrm{A}\mathrm{B}$$
  • $$\mathrm{A}\mathrm{B}\mathrm{A}\mathrm{B}$$
If $$A=\left[\begin{array}{lll}
1 & -2 & 3\\
-4 & 2 & 5
\end{array}\right]$$ and $$B=\left[\begin{array}{ll}
2 & 3\\
4 & 5\\
2 & 1
\end{array}\right],$$ then 
  • $$\mathrm{A}\mathrm{B},\ \mathrm{B}\mathrm{A}$$ exist and equal
  • $$\mathrm{A}\mathrm{B},\ \mathrm{B}\mathrm{A}$$ exist and are not equal
  • $$\mathrm{A}\mathrm{B}$$ exists and $$\mathrm{B}\mathrm{A}$$ does not exist
  • $$\mathrm{A}\mathrm{B}$$ does not exist and $$\mathrm{B}\mathrm{A}$$ exists
$$\left[\begin{array}{ll}
x & 0\\
0 & y
\end{array}\right]\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]=$$
  • $$\left[\begin{array}{ll} ax & b_{X}\\ yc & dy \end{array}\right]$$
  • $$\left[\begin{array}{ll} ax & 0\\ 0 & dy \end{array}\right]$$
  • $$\left[\begin{array}{ll} ay & cy\\ bx & dy \end{array}\right]$$
  • $$\left[\begin{array}{ll} 0& ax\\ dy & 0 \end{array}\right]$$
If $$\mathrm{A}=\left[\begin{array}{lll}
1 & -3 & -4\\
-1 & 3 & 4\\
1 & -3 & -4
\end{array}\right]$$, then $$\mathrm{A}^{2}=$$
  • $$A$$
  • $$- A$$
  • Null matrix
  • $$2A$$
If $$A=[x,y],  B=\left[\begin{array}{ll}
a & h\\
h & b
\end{array}\right],  C=\left[\begin{array}{l}
x\\
y
\end{array}\right]$$,
then $$\mathrm{A}\mathrm{B}\mathrm{C}=$$
  • $$(ax+hy+bxy)$$
  • $$(ax^{2}+2hxy+by^{2})$$
  • $$(ax^{2}-2hxy+by^{2})$$
  • $$(bx^{2}-2hxy+ay^{2})$$
If $$\mathrm{A}$$ is skew-symmetric matrix and $$\mathrm{n}$$ is even positive integer, then $$\mathrm{A}^{\mathrm{n}}$$ is
  • a symmetric matrix
  • skew-symmetric matrix
  • diagonal matrix
  • triangular matrix
If $$A=[1\ \  2\ \  3\ \  4]$$ and $$AB = [3 \ \ 4\ \  -1],$$ then the order of
matrix $$B$$ is 
  • $$2 \times 3$$
  • $$3\times 3$$
  • $$4 \times 3$$
  • $$1 \times 3$$
$$A=\begin{bmatrix}x& -7\\ 7& y\end{bmatrix}$$ is a skew-symmetric matrix,
then (x,y) = 
  • (1,-1)
  • (7,-7)
  • (0,0)
  • (14,-14)
$$A=\left[\begin{array}{lll} 0 & 1 & -2\\1 & 0 & 3\\2 &-3 & 0 \end{array}\right]$$ then $$\mathrm{A}+\mathrm{A}^{\mathrm{T}}=$$
  • $$\left[\begin{array}{lll}

    0 & 2 & 0\\

    2 & 0 & 0\\

    0 & 0 & 0

    \end{array}\right]$$
  • $$\left[\begin{array}{lll}

    1 & 0 & 0\\

    0 & 3 & 0\\

    0 & 0 & 4

    \end{array}\right]$$
  • $$\left[\begin{array}{lll}

    2 & 0 & 0\\

    0 & 2 & 0\\

    0 & 0 & 2

    \end{array}\right]$$
  • $$\left[\begin{array}{lll}

    2 & 0 & 2\\

    0 & 2 & 0\\

    0 & 0 & 2

    \end{array}\right]$$
The order of $$[\mathrm{x} \space \mathrm{y} \space\mathrm{z}] \left[\begin{array}{lll}
\mathrm{a} & \mathrm{h} & \mathrm{g}\\
\mathrm{h} & \mathrm{b} & \mathrm{f}\\
\mathrm{g} & \mathrm{f} & \mathrm{c}
\end{array}\right]\left[\begin{array}{l}
\mathrm{x}\\
\mathrm{y}\\
\mathrm{z}
\end{array}\right]$$ is
  • $$3\mathrm{x}1$$
  • $$1\mathrm{x}1$$
  • $$1\mathrm{x}3$$
  • $$3\mathrm{x}3$$
If $$A$$ and $$B$$ are two matrices such that $$A + B$$ and $$AB$$ are both defined, then 
  • $$A$$ and $$B$$ are two matrices not necessarily of same order
  • $$A$$ and $$B $$ are square matrices of same order
  • $$A$$ and $$B $$ are matrices of same type
  • $$A$$ and $$B$$ are rectangular matrices of same order
If the transpose of a matrix is equal to the additive
inverse, then matrix is called _________
matrix.

  • symmetric
  • skew symmetric
  • identity
  • inverse
If $$I = \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix},$$ then find $$I^3$$
  • $$1$$
  • $$I$$
  • $$0$$
  • does not exist
If $$A= \begin{bmatrix}
1 & 2 & 3\\
4 & 5 & 6
\end{bmatrix}$$ and $$B= \begin{bmatrix}
1\\
0\\

5\end{bmatrix},$$ then $$AB = $$
  • $$\begin{bmatrix}
    1 & 0 & 15
    \end{bmatrix}$$
  • $$\begin{bmatrix}
    4 & 0 & 30
    \end{bmatrix}$$
  • $$\begin{bmatrix}
    16\\

    34\end{bmatrix}$$
  • $$\begin{bmatrix}
    16 & 34
    \end{bmatrix}$$
If $$A = \begin{bmatrix}a & b\end{bmatrix},\space B = \begin{bmatrix}-b & -a \end{bmatrix}$$ and $$C = \begin{bmatrix}a \\ -a\end{bmatrix}$$, then the correct statement is
  • $$A = -B$$
  • $$A+B = A-B$$
  • $$AC = BC$$
  • $$CA = CB$$
If $$\displaystyle A = \begin{bmatrix} 1 & -2 & 4 \\ 2 & 3 & 2 \\ 3 & 1 & 5 \end{bmatrix}$$ and $$\displaystyle B = \begin{bmatrix} 0 & -2 & 4 \\ 1 & 3 & 2 \\ -1 & 1 & 5 \end{bmatrix}$$, then $$A + B$$ is
  • $$\displaystyle \begin{bmatrix}

    1 & -2 & 4 \\

    3 & 3 & 2 \\

    2 & 1 & 5

    \end{bmatrix}$$
  • $$\displaystyle \begin{bmatrix}

    1 & -2 & 8 \\

    3 & 3 & 4 \\

    2 & 1 & 10

    \end{bmatrix}$$
  • $$\displaystyle \begin{bmatrix}

    1 & -4 & 8 \\

    3 & 6 & 4 \\

    2 & 2 & 10

    \end{bmatrix}$$
  • none of these
If $$A=\begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix} $$, then $$ A^{3}-A^{2}=$$
  • $$2A$$
  • $$2I$$
  • $$A$$
  • $$I$$
If $$\begin{bmatrix}3 & -1 \\ 2 & 5\end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix} = \begin{bmatrix}4 \\ -3\end{bmatrix},$$ find $$x$$ and $$y$$
  • $$x=3,\space y = -1$$
  • $$x=2,\space y = 5$$
  • $$x=1,\space y = -1$$
  • $$x=-1,\space y = 1$$
If $$\displaystyle \:A= \left [ \begin{matrix}4 &x+2 \\2x-3  &x+1 \end{matrix} \right ]$$ is symmetric, then x= 
  • 3
  • 5
  • 2
  • 4
If $$\begin{bmatrix} 1 & 2 & 3   \end{bmatrix}   B=\begin{bmatrix}  3 & 4   \end{bmatrix}$$, then the order of the matrix $$B$$ is
  • $$3\times 1$$
  • $$1\times 3$$
  • $$2\times 3$$
  • $$3\times 2$$
If $$A=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$, then $$A^{4}=$$
  • $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 0 \\ 1 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$
Given that $$\displaystyle M=\begin{bmatrix}3 &-2 \\-4  &0 \end{bmatrix}\:and\:N=\begin{bmatrix}-2 &2 \\5  &0 \end{bmatrix}$$, then $$M+N$$ is a 
  • null matrix
  • unit matrix
  • $$\displaystyle \begin{bmatrix}

    1 & 0 \\1

    &0

    \end{bmatrix}$$
  • $$\displaystyle \begin{bmatrix}

    0 &1 \\1

    &1 

    \end{bmatrix}$$
If $$A=\begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$$ and $$B=\begin{bmatrix} 1 & 3 & 2 \\ 2 & 3 & 4 \end{bmatrix}$$, then $$AB$$ equal to 
  • $$\begin{bmatrix} 8 & 15 & 16 \\ 5 & 9 & 10 \end{bmatrix}$$
  • $$\begin{bmatrix} 8 & 5 \\ 15 & 9 \\ 16 & 10 \end{bmatrix}$$
  • $$\begin{bmatrix} 8 & 5 \\ 15 & 9 \end{bmatrix}$$
  • None of these
If $$A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end{bmatrix}$$, then $$A^2$$ is equal to 
  • $$A$$
  • $$-A$$
  • null matrix
  • $$I$$
0:0:1


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