CBSE Questions for Class 12 Commerce Maths Matrices Quiz 3 - MCQExams.com

If $$A = \begin{bmatrix} 2& 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$$, then $$A^6 =$$
  • $$6A$$
  • $$12A$$
  • $$16A$$
  • $$32A$$
Consider the following statements in respect of the matrix $$A = \begin{bmatrix} 0 & 1 & 2\\ -1 & 0  & -3 \\ -2 & 3 & 0 \end{bmatrix}$$ :
The matrix A is skew-symmetric.
The matrix A is symmetric.
The matrix A is invertible.
Which of the above statements is/are correct ? 
  • 1 only
  • 3 only
  • 1 and 3
  • 2 and 3
If the sum of the matrices $$\begin{bmatrix} x \\ x \\ y \end{bmatrix},\begin{bmatrix} y \\ y \\ z \end{bmatrix}$$ and $$\begin{bmatrix} z \\ 0 \\ 0 \end{bmatrix}$$ is the matrix $$\begin{bmatrix} 10 \\ 5 \\ 5 \end{bmatrix}$$, then what is the value of  $$y$$?
  • $$-5$$
  • $$0$$
  • $$5$$
  • $$10$$
If $$A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$$, $$B = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$$, then $$BA =$$
  • $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$$
If $$A$$ and $$B$$ are square matrices such that $$AB = I$$ and $$BA = I$$, then $$B$$ is
  • Unit matrix
  • Null matrix
  • Multiplicative inverse matrix of $$A$$
  • $$- A$$
What is $$\begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a& h & g\\ h & b & f\\ g & f & c\end{bmatrix}$$ equal to?
  • $$\begin{bmatrix}ax + hy + gz & h + b + f & g + f + c\end{bmatrix}$$
  • $$\begin{bmatrix}a & h & g\\ hx & by & fz\\ g & f & c\end{bmatrix}$$
  • $$\begin{bmatrix}ax & hy & gz\\ hx & by & fz\\ gx & fy & cz\end{bmatrix}$$
  • $$\begin{bmatrix} ax + hy + gz & hx + by + fz & gx + fy + cz\end{bmatrix}$$
If $$A$$ is any matrix, then the product $$AA$$ is defined only when A is a matrix of order $$m \times n$$ where : 
  • $$m > n $$
  • $$m < n$$
  • $$m=n $$
  • $$m \leq n $$
Consider the following statements:
The product of two non-zero matrices can never be identity matrix.
The product of two non-zero matrices can never be zero matrix.
Which of the above statements is/are correct?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
If $$[2\ 3\ 4] \begin{bmatrix}1 & x &3 \\ 2 & 4 & 5\\ 3 & 2 &x \end{bmatrix} \begin{bmatrix} x\\ 2 \\  0 \end{bmatrix} = 0$$, then $$x =$$ ________.
  • $$\dfrac {7}{3}$$
  • $$\dfrac {5}{3}$$
  • $$-\dfrac {5}{3}$$
  • $$-\dfrac {7}{3}$$
If $$A=\begin{bmatrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \end{bmatrix}$$ is a symmetric matrices then $$x=$$
  • $$0$$
  • $$3$$
  • $$6$$
  • $$8$$
Given $$A$$ is a matrix of order $$3\times 2$$. If order of $$AB$$ is $$3\times 3$$, then order of $$B$$ will be 
  • $$1\times 3$$
  • $$2\times 3$$
  • $$3\times 3$$
  • $$2\times 2$$
The inverse of $$\begin{bmatrix} 1 & a & b \\ 0 & x & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ is $$\begin{bmatrix} 1 & -a & -b \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ then $$x=$$
  • $$a$$
  • $$b$$
  • $$0$$
  • $$1$$
Given $$A= \begin{bmatrix}  3&4  \\ 4&-3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 24 \\ 7\end{bmatrix},$$ find the matrix $$X$$ such that $$AX=B$$.
  • $$\begin{bmatrix} -4 \\ -3\end{bmatrix}$$
  • $$\begin{bmatrix} 4 \\ 3\end{bmatrix}$$
  • $$\begin{bmatrix} -4 \\ 3\end{bmatrix}$$
  • $$\begin{bmatrix} 4 \\ -3\end{bmatrix}$$
If $$A=\begin{bmatrix} \cos { x }  & \sin { x }  \\ -\sin { x }  & \cos { x }  \end{bmatrix}$$ and $$A(AdjA)=k\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ then the value of $$k$$ is
  • $$\sin{x}\cos{x}$$
  • $$1$$
  • $$-1$$
  • $$2$$
If $$A=\begin{bmatrix} 0 & a+1 & b-2 \\ 2a-1 & 0 & c-2 \\ 2b+1 & 2+c & 0 \end{bmatrix}$$ is skew symmetric then $$a+b+c$$=
  • $$3$$
  • $$-3$$
  • $$\cfrac{1}{3}$$
  • $$-\cfrac{1}{3}$$
If $$A = \left[ {\begin{array}{*{20}{c}}  2&{ - 3} \\   { - 4}&1 \end{array}} \right]$$, then $$\left[ {3{A^2} + 12A} \right]$$ is equal to 
  • $$\left[ {\begin{array}{*{20}{c}}
    {72}&{ - 84} \\
    { - 63}&{51}
    \end{array}} \right]$$
  • $$\left[ {\begin{array}{*{20}{c}}
    {51}&{63} \\
    {84}&{72}
    \end{array}} \right]$$
  • $$\left[ {\begin{array}{*{20}{c}}
    {51}&{84} \\
    {63}&{72}
    \end{array}} \right]$$
  • $$\left[ {\begin{array}{*{20}{c}}
    {72}&{ - 63} \\
    { - 84}&{51}
    \end{array}} \right]$$
The Inverse of a square matrix, if it exist is unique.
  • True
  • False
$$A=\begin{bmatrix} a & b \\ 0 & c \end{bmatrix}$$ then $${A}^{-1}+(A-aI)(A-cI)=$$
  • $$\cfrac { 1 }{ ac } \begin{bmatrix} a & b \\ 0 & -c \end{bmatrix}$$
  • $$\cfrac { 1 }{ ac } \begin{bmatrix} -a & b \\ 0 & c \end{bmatrix}$$
  • $$\cfrac { 1 }{ ac } \begin{bmatrix} c & -b \\ 0 & a \end{bmatrix}$$
  • $$\cfrac { 1 }{ ac } \begin{bmatrix} c & b \\ 0 & a \end{bmatrix}$$
If $$A$$ is square  matrix such that $${A^2} = 1$$ then $${A^{ - 1}} = ?$$
  • $$2$$A
  • A
  • $$0$$
  • A+$$1$$
If $$A=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{bmatrix}$$ then $$A^ {2}$$ is equal to 
  • $$A$$
  • $$-A$$
  • $$2A$$
  • $$-2A$$
If $$A=\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$$ then $$A^{100}$$=..............
  • 100A
  • $$2^{99}A$$
  • $$2^{100}A$$
  • 99A
iF $$A=\begin{bmatrix}  1&  -1\\  -1&  1\end{bmatrix}$$, then the expression $$A^3-2A^2$$ is 
  • a null matrix
  • an identity matrix
  • equal to A
  • equal to -A
State true/false:
Matrices of any order can be added.
  • True
  • False
lf $$\left[\begin{array}{ll}
x & 1\\
1 & y
\end{array}\right]\left[\begin{array}{ll}
1 & 4\\
2 & 6
\end{array}\right] =\left[\begin{array}{ll}
4 & 14\\
7 & 22
\end{array}\right]$$, then $$(x,y)$$$$=$$
  • $$(1,-2)$$
  • $$( 2,1)$$
  • $$(3,2)$$
  • $$(2,3)$$
If $$D_{1}$$ and $$D_{2}$$ are two 3 x 3 diagonal matrices, then 
  • $$D_{1}D_{2}$$ is a diagonal matrix
  • $$D_{1}+D_{2}$$ is a diagonal matrix
  • $$D_{1}^{2}+D_{2}^{2}$$ is a diagonal matrix
  • 1, 2, 3 are correct
$$\left[\begin{array}{lll}
x & 0 & 0\\
y & \mathrm{z} & 0\\
l & m & n
\end{array}\right]\left[\begin{array}{lll}
a & 0 & 0\\
0 & b & 0\\
0 & 0 & c
\end{array}\right] =$$
  • $$\left[\begin{array}{lll} ax & 0 & 0\\ ay & b_{Z} & 0\\ al & mb & nc \end{array}\right]$$
  • $$\left[\begin{array}{lll} 0 & 0 & nc\\ 0 & b_{Z} & mb\\ a\mathrm{x} & ab & al \end{array}\right]$$
  • $$\left[\begin{array}{lll} a\mathrm{x} & ab & al\\ 0 & b_{Z} & mb\\ 0 & 0 & nc \end{array}\right]$$
  • None of these
$$A=\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$$, then $$A^{2}=$$
  • $$\begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$$
  • $$\begin{bmatrix} 5 & -8 \\ 2 & -3 \end{bmatrix}$$
  • $$\begin{bmatrix} { 3 } & { -4 } \\ { 2 } &  -1 \end{bmatrix}$$
  • None of these
If $$A=\begin{bmatrix} a & b \\ b & a \end{bmatrix}$$ and $${ A }^{ 2 }=\begin{bmatrix} \alpha  & \beta  \\ \beta  & \alpha  \end{bmatrix}$$, then
  • $$\alpha ={ a }^{ 2 }+{ b }^{ 2 },\beta =2ab$$
  • $$\alpha ={ a }^{ 2 }+{ b }^{ 2 },\beta ={ a }^{ 2 }-{ b }^{ 2 }$$
  • $$\alpha =2ab,\beta ={ a }^{ 2 }+{ b }^{ 2 }$$
  • $$\alpha ={ a }^{ 2 }+{ b }^{ 2 },\beta =ab$$
If $$A=[a_{ij}]_{3\times 3}$$ is a square matrix so that $$a_{ij}=i^{2}-j^{2}$$, then $$A$$ is a  
  • unit matrix
  • symmetric marix
  • skew symmetric matrix
  • orthogonal matrix
If $$\mathrm{A}= \left[\begin{array}{lll}
2 & 0 & 0\\
0 & 2 & 0\\
0 & 0 & 2
\end{array}\right]$$, then $$\mathrm{A}^{4}$$ is equal to 
  • $$16\mathrm{A}$$
  • $$32 \mathrm A$$
  • $$4\mathrm{A}$$
  • $$8\mathrm{A}$$
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