CBSE Questions for Class 12 Commerce Maths Matrices Quiz 11 - MCQExams.com

If $$A = \begin{bmatrix}1 & 2 & x\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}$$ and $$B = \begin{bmatrix}1 & -2 & y\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}$$ and $$AB = I_{3}$$, then $$x + y=$$ _____.
  • $$0$$
  • $$-1$$
  • $$2$$
  • None of these
If $$A = \begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ a & b & -1\end{bmatrix}$$, then $$A^{2}$$ is equal to
  • null matrix
  • unit matrix
  • $$-A$$
  • $$A$$
If $$ \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}A\begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}  $$ , then A = 
  • $$ \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix} $$
  • $$ \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} $$
  • $$ \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} $$
  • $$ - \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix} $$
If $$ \begin{bmatrix} 1/25 & 0 \\ x & 1/25 \end{bmatrix}\quad =\quad \begin{bmatrix} 5 & 0 \\ -a & 5 \end{bmatrix}^{ -2 } $$, then the value of x is 
  • $$ a / 125 $$
  • $$ 2a / 125 $$
  • $$ 2a / 25 $$
  • None of these
If $$ AB =  A $$ and  $$ BA =B, $$ then 
  • $$ A^2 B = A^2 $$
  • $$ B^2A =B^2 $$
  • $$ ABA = A $$
  • $$ BAB = B $$
If $$A = \begin{bmatrix}3 &-4 \\ -1 & 2\end{bmatrix}$$ and $$B$$ is a square matrix of order $$2$$ such that $$AB = I$$ then $$B = ?$$
  • $$\begin{bmatrix}1 &2 \\ 2 & 3\end{bmatrix}$$
  • $$\begin{bmatrix}1 &\dfrac {1}{2} \\ 2 & \dfrac {3}{2}\end{bmatrix}$$
  • $$\begin{bmatrix}1 &2 \\ \dfrac {1}{2} & \dfrac {3}{2}\end{bmatrix}$$
  • None of these
Find the value of $$x,$$ if $$\left [ 1\ x\ 1 \right ]$$ $$\begin{bmatrix} 1 & 3 & 2 \\  2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix}$$ $$\begin{bmatrix}1 \\ 2 \\ x \end{bmatrix}=O.$$
  • $$-2$$
  • $$2$$
  • $$-14$$
  • 9
The matrix $$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix}$$ is a 
  • Identity matrix
  • Symmetric matrix
  • Skew symmetric matrix
  • None of these
If matrix $$A=[a_{ij}]_{2\times 2}$$, where $$a_{ij} *1$$ if $$1*j$$ and $$0$$ if $$i=j$$ then $$A^2$$ is equal to
  • $$I$$
  • $$A$$
  • $$0$$
  • $$None\ of\ these$$
$$AA^{'}$$ is always a symmetric matrix for any matrix $$A$$.
  • True
  • False
If $$A$$ and $$B$$ are square matrices of the same order, then $$(A+B)(A-B)$$ is equal to 
  • $$A^2-B^2$$
  • $$A^2-BA-AB-B^2$$
  • $$A^2-B^2+BA-AB$$
  • $$A^2-BA+B^2+AB$$
If $$A=\begin{bmatrix} 2 & 1 & 3 \\ 4 & 5 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 2 & 3 \\ 4 & 2 \\ 1 & 5 \end{bmatrix}$$, then 
  • Only $$AB$$ is defined
  • only $$BA$$ is defined
  • $$AB$$ and $$BA$$ both are defined
  • $$AB$$ and $$BA$$ both are not defined
State true/false:
If $$A$$ and $$B$$ are two matrices of orders $$  3 \times 2 $$ and $$ 2 \times 3 $$ respectively, then their sum $$ A + B $$ is possible.
  • True
  • False
If A=$$\displaystyle \begin{vmatrix} a & b &c  \\ x & y & z \\ l & m & n \end{vmatrix}$$ is a skew-symmetric matrix then which of the following is equal to x+y+z?
  • $$a+b+c$$
  • $$l+m+n$$
  • $$-b-m$$
  • $$c-l-n$$
Given $$A =\begin{bmatrix} 2& 1\\2 &1 \end{bmatrix} .$$ Find all possible matrix $$X$$ for which $$AX = A.$$
  • $$X =\begin{bmatrix} a&b \\ 2 -2a&1 -2b\end{bmatrix}$$ for a, $$b\in R$$
  • $$X =\begin{bmatrix} b&a \\ 2 -2b&1 -2a\end{bmatrix}$$ for a, $$b\in R$$
  • $$X =\begin{bmatrix} b&a \\ 1 -2a&2 -2b\end{bmatrix}$$ for a, $$b\in R$$
  • none of these
If $$\alpha ,\beta ,\gamma $$ are three real numbers and $$A=\begin{bmatrix} 1&\cos (\alpha -\beta )  &\cos (\alpha -\gamma ) \\\cos (\beta -\alpha )  &1  & \cos (\beta -\gamma ) \\ \cos (\gamma  -\alpha )  & \cos (\gamma  -\beta  ) &1 \end{bmatrix}$$ then
  • $$A$$ is symmetric
  • $$A$$ is orthogonal
  • $$A$$ is singular
  • $$A$$ is not invertible.
Let $$\alpha =\pi /5$$ and
   $$A=\begin{bmatrix}\cos \alpha & \sin \alpha \\-\sin \alpha &\cos \alpha  \end{bmatrix}$$ and $$B = A + A^2 + A^3 + A^4$$ , then 
  • singular
  • non-singular
  • skew-symmetric
  • $$|B|=1$$
If the matrix $$A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{bmatrix}$$, then $$A^n=\begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ b & 0 & a\end{bmatrix}. n \in N$$ where
  • $$a = 2n, b = 2^n$$
  • $$a = 2^n, b = 2n$$
  • $$a = 2^n, b = n2^{n-1}$$
  • $$a = 2^n, b = n2^n$$
If $$3\begin{bmatrix}2 & 3\\ -4 & 1\end{bmatrix} - 2 \begin{bmatrix} x& y\\ 3 & 4\end{bmatrix} = \begin{bmatrix}10 & 11\\ z & -5\end{bmatrix}$$, then $$x + y - z =$$
  • $$-21$$
  • $$-15$$
  • $$0$$
  • $$15$$
  • $$21$$
If $$O\left( A \right) =2\times 3,$$ $$O\left( B \right) =3\times 2$$ and $$O\left( C \right) =3\times 3$$, which one of the following is not defined?
  • $$CB+{ A }^{ ' }$$
  • $$BAC$$
  • $$C{ \left( A+{ B }^{ ' } \right) }^{ ' }$$
  • $$C\left( A+{ B }^{ ' } \right) $$
$$A $$ is of order $$m \times n$$ and $$B$$ is of order $$p \times q,$$ addition of $$A$$ and $$B$$ is possible only if
  • $$m = p$$
  • $$n = q$$
  • $$n = p$$
  • $$m = p, n = q$$
Let $$A=\begin{bmatrix} 3 & 1\\ -1 & 2\end{bmatrix}$$, then
  • $$A^2+7A-5I=0$$
  • $$A^2-7A+5I=0$$
  • $$A^2+5A-7I=0$$
  • $$A^2-5A+7I=0$$
What is the inverse of the matrix
$$A=\begin{bmatrix} \cos { \theta  }  & \sin { \theta  }  & 0 \\ -\sin { \theta  }  & \cos { \theta  }  & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ ?
  • $$\begin{bmatrix} \cos { \theta } & -\sin { \theta } & 0 \\ \sin { \theta } & \cos { \theta } & 0 \\ 0 & 0 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} \cos { \theta } & 0 & -\sin { \theta } \\ 0 & 1 & 0 \\ \sin { \theta } & 0 & \cos { \theta } \end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos { \theta } & -\sin { \theta } \\ 0 & \sin { \theta } & \cos { \theta } \end{bmatrix}$$
  • $$\begin{bmatrix} \cos { \theta } & \sin { \theta } & 0 \\ -\sin { \theta } & \cos { \theta } & 0 \\ 0 & 0 & 1 \end{bmatrix}$$
If $$A=
\begin{bmatrix}
2 & -1 \\
-1 & 2
\end{bmatrix}$$ and $$I$$ is the unit matrix of order $$2$$, then $$A^2$$equals
  • $$4A-3I$$
  • $$3A-AI$$
  • $$A-I$$
  • $$A+I$$
Let $$A=\begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$$ and $$10B=\begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha  \\ 1 & -2 & 3 \end{bmatrix}$$. If $$B$$ is the inverse of matrix $$A$$, then $$\alpha $$ is
  • $$-2$$
  • $$1$$
  • $$2$$
  • $$5$$
$$If\quad A=\begin{bmatrix} ab & { b }^{ 2 } \\ -{ a }^{ 2 } & -ab \end{bmatrix},then\quad { A }^{ 2 }\quad is\quad equal\quad to$$
  • $$O$$
  • $$I$$
  • $$-I$$
  • $$None\quad of\quad these$$
The value of $$x$$, so that $$\left[ 1 \quad x \quad 1 \right] \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{bmatrix}\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0$$ is/are
  • $$\pm\ 2$$
  • $$0$$
  • $$\dfrac { -7\pm \sqrt { 35 } }{ 2 }$$
  • $$\dfrac { -9\pm \sqrt { 53 } }{ 2 }$$
If the matrix $$\begin{bmatrix} 0 & 2\beta & \Upsilon \\ \alpha & \beta & -\Upsilon \\ \alpha & -\beta & \Upsilon \end{bmatrix}$$is orthogonal, then
  • $$\alpha = \pm\dfrac{1}{\sqrt{2}}$$
  • $$\beta = \pm\dfrac{1}{\sqrt{6}}$$
  • $$\gamma = \pm\dfrac{1}{\sqrt{3}}$$
  • all of these
If $$\left[ \begin{matrix} x & 4 & -1 \end{matrix} \right] \left[ \begin{matrix} 2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4 \end{matrix} \right] \left[ \begin{matrix} x \\ 4 \\ -1 \end{matrix} \right] =0,$$ then $$x=$$
  • $$-1+\sqrt { 6 } $$
  • $$8\pm \sqrt { 5 } $$
  • $$-2\pm \sqrt { 10 } $$
  • $$3\pm \sqrt { 6 } $$
If $$A=\begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}$$, then : $$A^{-1}$$=
  • $$A$$
  • $$A^{2}$$
  • $$A^{3}$$
  • $$A^{4}$$
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