CBSE Questions for Class 12 Commerce Maths Matrices Quiz 7 - MCQExams.com

Say true or false:
If $$A$$, $$B$$ be two matrices such that they commute, then $$A^2 - B^2 = (A - B)(A + B)$$.
  • True
  • False
If $$A=\begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}$$, then $$(A-2I)(A-3I)=$$ 
  • $$0$$
  • $$A$$
  • $$I$$
  • $$5I$$
If $$\displaystyle A\times \begin{bmatrix} 1 & 2 &3  \\ 4 & 5 & 6  \end{bmatrix}=\begin{bmatrix} 1 & 2 &3  \\ 3 & 2 & 1 \\ 3 & 1 & 2 \end{bmatrix}$$ then the order of A is _______
  • $$\displaystyle 2\times 3$$
  • $$\displaystyle 3\times 3$$
  • $$\displaystyle 3\times 2$$
  • $$\displaystyle 2\times 2$$
Inverse of a diagonal matrix is
  • Symmetric
  • A skew-symmetric
  • A diagonal matrix
  • None of these
If $$A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$, then $$A^2 - 5A$$ is equal to 
  • $$2I$$
  • $$-2I$$
  • $$3I$$
  • Null matrix
If $$A+I=\begin{bmatrix} 3 & -2 \\ 4 & 1 \end{bmatrix}$$, then $$\left( A+I \right) \cdot \left( A-I \right) $$ is equal to
  • $$\begin{bmatrix} -5 & -4 \\ 8 & -9 \end{bmatrix}$$
  • $$\begin{bmatrix} -5 & 4 \\ -8 & 9 \end{bmatrix}$$
  • $$\begin{bmatrix} 5 & 4 \\ 8 & 9 \end{bmatrix}$$
  • $$\begin{bmatrix} -5 & -4 \\ -8 & -9 \end{bmatrix}$$
Two matrices $$A$$ and $$B$$ are multiplied to get $$AB$$ if
  • both are rectangular
  • both have same order
  • number of columns of $$A$$ is equal to rows of $$B$$
  • number of rows of $$A$$ is equal to no of columns of $$B$$
If $$A=\begin{bmatrix} 2 & -1 & 1 \\ -2 & 3 & -2 \\ -4 & 4 & -3 \end{bmatrix}$$, then $${ A }^{ 2 }$$ is equal to
  • Null matrix
  • Itself $$A$$
  • Unit matrix
  • Scalar matrix
If $$\displaystyle A=\left[ \begin{matrix} 2 \\ 0 \\ 0 \end{matrix}\,\,\,\begin{matrix} 0 \\ 2 \\ 0 \end{matrix}\,\,\,\begin{matrix} 0 \\ 0 \\ 2 \end{matrix} \right] $$ then $$\displaystyle { A }^{ 5 }=$$
  • $$\displaystyle 5A$$
  • $$\displaystyle 10A$$
  • $$\displaystyle 16A$$
  • $$\displaystyle 32A$$
If $$A$$ and $$B$$ are symmetric matrices, then $$ABA$$ is
  • Symmetric
  • Skew-symmetric
  • Diagonal
  • Triangular
If $$A$$ is an $$m \times n$$ matrix such that $$AB$$ and $$BA$$ are both defined, then order of $$B$$ is
  • $$m \times n$$
  • $$n \times m$$
  • $$n \times n$$
  • $$m \times m$$
If $$\displaystyle A=\begin{bmatrix} 0 & 0 & 1\\ 0 & 1&0 \\ 1& 0 & 0\end{bmatrix}$$, then $$A^{-1}$$ is.
  • $$-A$$
  • $$A$$
  • $$1$$
  • None of these
If $$A=\begin{bmatrix}1 & 1\\ 1& 1\end{bmatrix}$$, then $$A^{100}$$ is equal to.
  • $$2^{100}A$$
  • $$2^{99}A$$
  • $$100A$$
  • $$299A$$
If $$\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}$$, then $${A}^{-1}$$ is equal to
  • $$\begin{bmatrix} \cfrac { 5 }{ 11 } & \cfrac { 2 }{ 11 } \\ \cfrac { 3 }{ 11 } & -\cfrac { 1 }{ 11 } \end{bmatrix}$$
  • $$\begin{bmatrix} -\cfrac { 5 }{ 11 } & -\cfrac { 2 }{ 11 } \\ -\cfrac { 3 }{ 11 } & -\cfrac { 1 }{ 11 } \end{bmatrix}$$
  • $$\begin{bmatrix} \cfrac { 5 }{ 11 } & \cfrac { 2 }{ 11 } \\ \cfrac { 3 }{ 11 } & \cfrac { 1 }{ 11 } \end{bmatrix}$$
  • $$\begin{bmatrix} 5 & 2 \\ 3 & -1 \end{bmatrix}$$
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
  • $$-2$$
  • $$1$$
  • $$2$$
  • $$5$$
Inverse of the matrix $$\begin{bmatrix} \cos 2\theta & -\sin 2\theta\\ \sin 2\theta & \cos 2\theta\end{bmatrix}$$ is.
  • $$\begin{bmatrix} \cos 2\theta & -\sin 2\theta\\ \sin 2\theta & \cos 2\theta\end{bmatrix}$$
  • $$\begin{bmatrix} \cos 2\theta & \sin 2\theta\\ \sin 2\theta & -\cos 2\theta\end{bmatrix}$$
  • $$\begin{bmatrix} \cos 2\theta & \sin 2\theta\\ \sin 2\theta & \cos 2\theta\end{bmatrix}$$
  • $$\begin{bmatrix} \cos 2\theta & \sin 2\theta\\ -\sin 2\theta & \cos 2\theta\end{bmatrix}$$
If $$A=\begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$$ and $$B=\begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$$, then $${ \left( AB \right)  }^{ T }$$ is equal to
  • $$\begin{bmatrix} -3 & -2 \\ 10 & 7 \end{bmatrix}$$
  • $$\begin{bmatrix} -3 & 10 \\ -2 & 7 \end{bmatrix}$$
  • $$\begin{bmatrix} -3 & 7 \\ 10 & 2 \end{bmatrix}$$
  • None of these
If $$\begin{bmatrix}1 & 1 &1\\ 1&-2 &-2\\1 & 3 &1\end{bmatrix}$$ $$\begin{bmatrix} x\\ y\\z\end{bmatrix}=\begin{bmatrix} 0 \\ 3\\4\end{bmatrix}$$, then $$\begin{bmatrix} x\\ y\\z\end{bmatrix}$$ is equal to.
  • $$\begin{bmatrix} 0\\1\\1\end{bmatrix}$$
  • $$\begin{bmatrix} 1\\2\\-3\end{bmatrix}$$
  • $$\begin{bmatrix} 5\\-2\\1\end{bmatrix}$$
  • $$\begin{bmatrix} 1\\-2\\3\end{bmatrix}$$
$$A=\begin{bmatrix} -2&4\\-1&2  \end{bmatrix}$$, then $$A^2$$ is equal to 
  • Null matrix
  • Unit matrix
  • $$\begin{bmatrix} 1&0\\0&1 \end{bmatrix}$$
  • $$\begin{bmatrix} 0&0\\0&1 \end{bmatrix}$$
If $$A=[x\, y\, z], B = \begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}$$ and $$C=\begin{bmatrix}x\\y\\z\end{bmatrix}$$
Then, $$ABC = 0$$, if
  • $$[ax^2+by^2+cz^2+2gxy+2fyz+2czx]=0$$
  • $$[ax^2+cy^2+bz^2+xy+yz+zx]=0$$
  • $$[ax^2+by^2+cz^2+2hxy+2by+2cz]=0$$
  • $$[ax^2+by^2+cz^2+2gzx+2fyz+2hxy]=0$$
If $$A$$ and $$B$$ are any two matrices, then 
  • $$AB=BA$$
  • $$AB=I$$
  • $$AB=0$$
  • $$AB$$ may or may not be defined
If $$P=\begin{pmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{pmatrix}$$, then $${P}^{5}$$ is equal to
  • $$P$$
  • $$2P$$
  • $$-P$$
  • $$-2P$$
If $$A =\begin{bmatrix} 2 & -1 \\ -1 & 2  \end{bmatrix}$$ and $$I$$ is the unit matrix of order $$2$$, then $$A^2$$ equals
  • $$4A - 3I$$
  • $$3A - 4I$$
  • $$A - I$$
  • $$A + I$$
If $$A$$ is a matrix such that $$\begin{pmatrix}2&1 \\3&2 \end{pmatrix} A(1 \space  \,1)=\begin{pmatrix}1&1 \\0&0 \end{pmatrix}$$ then $$A= $$
  • $$\begin{pmatrix}1&1 \\0&1 \end{pmatrix}$$
  • $$(2 \,1)$$
  • $$\begin{pmatrix}1&0 \\-1&1 \end{pmatrix}$$
  • $$\begin{pmatrix}2 \\-3 \end{pmatrix}$$
For the matrices $$A=\begin{bmatrix} 1 & 3 \\ 0 & -1 \end{bmatrix}$$ $$B=\begin{bmatrix} 2 & 2 \\ -1 & 4 \end{bmatrix}$$
What is $$AB$$?
  • $$\begin{bmatrix} 3 & 5 \\ -1 & 3 \end{bmatrix}$$
  • $$\begin{bmatrix} 1 & -1 \\ -1 & 5 \end{bmatrix}$$
  • $$\begin{bmatrix} -1 & 14 \\ 1 & -4 \end{bmatrix}$$
  • $$\begin{bmatrix} 2 & 4 \\ -1 & -7 \end{bmatrix}$$
  • none of the above
The symmetric part of the matrix A= $$\begin{bmatrix}
1 &2  &4 \\
6 & 8 & 2\\
2 & -2 &7
\end{bmatrix}$$.
  • $$\begin{bmatrix}

    1 &4 &3 \\

    2 & 8 & 0\\

    3 & 0 &7

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

    1 &4 &3 \\

    4 & 8 & 0\\

    3 & 0 &7

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

    0 &-2 &-1 \\

    -2 & 0 & -2\\

    -1 & -2 &0

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

    0 &-2 &-1 \\

    2 & 0 & 2\\

    -1 & 2 &0

    \end{bmatrix}$$
If $$A = \begin{bmatrix} 0& 1\\ 1 & 0\end{bmatrix}$$, then $$A^{2}$$ is equal to ______
  • $$\begin{bmatrix} 0& 1\\ 1 & 0\end{bmatrix}$$
  • $$\begin{bmatrix} 1& 0\\ 1 & 0\end{bmatrix}$$
  • $$\begin{bmatrix} 1& 0\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 0& 1\\ 0 & 1\end{bmatrix}$$
$$\begin{bmatrix} 3& 2\\ -1 & -2\\ 4 & 5\end{bmatrix} \begin{bmatrix} 0& a\\ b & c \end{bmatrix} = \begin{bmatrix}-4 &9 \\ 4 & -7\\ -10 & 19\end{bmatrix}$$
Find $$a, b$$ and $$c$$.
  • $$2, -1, 3$$
  • $$1, -2, 3$$
  • $$3, -2, 1$$
  • $$1, 2, 3$$
If $$P=\begin{pmatrix}2&-2&-4 \\-1&3&4\\1&-2&-3\end{pmatrix}$$ then $$P^5$$ equals
  • $$P$$
  • $$2P$$
  • $$-P$$
  • $$-2P$$
For a matrix $$A \begin{pmatrix} 1& 0 & 0\\ 2 & 1 & 0\\ 3 & 2 & 1\end{pmatrix}$$, if $$U_{1}, U_{2}$$ and $$U_{3}$$ are $$3\times 1$$ column matrices satisfying $$AU_{1} = \begin{pmatrix}1\\ 0 \\ 0
\end{pmatrix}, AU_{2} \begin{pmatrix}2\\3 \\ 0
\end{pmatrix}, AU_{3} = \begin{pmatrix}2\\ 3\\ 1
\end{pmatrix}$$ and $$U$$ is $$3\times 3$$ matrix whose columns are $$U_{1}, U_{2}$$ and $$U_{3}$$
Then sum of the elements of $$U^{-1}$$ is
  • $$6$$
  • $$0 (zero)$$
  • $$1$$
  • $$2/3$$
0:0:1


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