CBSE Questions for Class 12 Commerce Maths Matrices Quiz 10 - MCQExams.com

If $$A = \left[ \begin{array} { c c } { a b } & { b ^ { 2 } } \\ { - a ^ { 2 } } & { - a b } \end{array} \right]$$ and $$A ^ { n } = 0$$ then the minimum value of $$n$$ is
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
If $$A=\left[ \begin{matrix} a & b \\ b & a \end{matrix} \right] $$ and $$A^{2}=\left[ \begin{matrix} \alpha  & \beta  \\ \beta  & \alpha  \end{matrix} \right] $$ 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 $$A=\left[ \begin{matrix} 6 & 9 \\ -4 & -6 \end{matrix} \right] $$, then $$A^{2}$$=
  • $$\left[ \begin{matrix} 6 & 9 \\ -4 & 6 \end{matrix} \right]$$
  • $$\left[ \begin{matrix} 6 & 9 \\ 4 & -6 \end{matrix} \right]$$
  • $$\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right]$$
  • $$\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix} \right]$$
If the order of $$A$$ is $$4 \times 3$$, the order of $$B$$ is $$4 \times 5$$ and the order of $$C ,\ 7\times 3$$ then the order of $$(A^{T}B^{T})^{T}C^{T}$$ is
  • $$4 \times 5$$
  • $$3 \times 7$$
  • $$4 \times 3$$
  • $$5 \times 7$$
If $$\left[ \begin{matrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{matrix} \right] =\left[ \begin{matrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{matrix} \right] ,$$ then 
  • $$a =4$$
  • $$a =1$$
  • $$b =4$$
  • $$b=1$$
The inverse of a symmetric matrix is
  • symmetric
  • skew-symmetric
  • diagonal matrix
  • singular matrix
If $$A = \left[ {\begin{array}{*{20}{c}}1&2\\3&4\end{array}} \right]$$, then $$8A^{-4}$$ is equal to
  • $$145A^{-1}+27I$$
  • $$145A^{-1}-27I$$
  • $$27I - 145A^{-1}$$
  • $$29A^{-1} +9I$$
If $$A=\left[ \begin{matrix} 1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7 \end{matrix} \right]$$ and $$A^{-1}=[\alpha_{ij}]_{3\times 3}$$ then $$\alpha_{23}=$$
  • $$-1/5$$
  • $$1/5$$
  • $$-2/5$$
  • $$2/5$$
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 $$\begin{bmatrix} 3 & 2 & -1 \\ 4 & 9 & 2 \\ 5 & 0 & -2 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 7 \\ 2 \end{bmatrix}$$, then $$(x,\ y,\ z)=$$ 
  • $$(1,\ -1,\ 1)$$
  • $$(2,\ -1,\ -4)$$
  • $$(3,\ 0,\ 6)$$
  • $$(2,\ -1,\ 4)$$
If A is a 2 X 2 matrix such that $$A^{2009} + A^{2008}$$= I, then : $$(A^{2008})^{-1}$$= 
  • $$A^{2008} + I$$
  • $$A^{2009} + 1$$
  • A + I
  • A
If $$\left[ \begin{matrix} 2 & -3 \\ 1 & \lambda  \end{matrix} \right] \times \left[ \begin{matrix} 1 & 5 & \mu  \\ 0 & 2 & -3 \end{matrix} \right] =\left[ \begin{matrix} 2 & 4 & 1 \\ 1 & -1 & 13 \end{matrix} \right],$$ then
  • $$\lambda=3, \mu= -4$$
  • $$\lambda=4, \mu=-3$$
  • no real values of $$\lambda, \mu$$ are possible
  • none of these
Let p be a non-singular matrix, $$1+p+p^{2}+....+p^{n}=0$$ (0 denotes the null matrix) then $$p^{-1}=$$
  • $$p^{n}$$
  • -$$p^{n}$$
  • -(1+p+...+$$p^{n}$$)
  • none
If $$A=\begin{bmatrix} 4 & -1 \\ -1 & k \end{bmatrix}$$ such that $$A^{2}-6A+7I=0$$, then $$k=$$
  • $$1$$
  • $$3$$
  • $$2$$
  • $$4$$
If $$A\begin{bmatrix} 1 & 1\\ 2 & 0\end{bmatrix}=\begin{bmatrix} 3 & 2\\ 1 & 1\end{bmatrix}$$, then $$A^{-1}$$ is given by?
  • $$\begin{bmatrix} 0 & -1\\ 2 & -4\end{bmatrix}$$
  • $$\begin{bmatrix} 0 & -1\\ -2 & -4\end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 1\\ 2 & -4\end{bmatrix}$$
  • None of these
A is an involuntary matrix given by $$A=\begin{bmatrix} 0 & 1 & -1\\ 4 & -3 & 4\\ 3 & -3 & 4\end{bmatrix}$$ then the inverse of $$\dfrac{A}{2}$$ will be?
  • $$2A$$
  • $$\dfrac{A^{-1}}{2}$$
  • $$\dfrac{A}{2}$$
  • $$A^{-2}$$
A is an involutory matrix given by $$A=\begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix}$$ then the inverse of $$\dfrac{A}{2}$$ will be 
  • $$2A$$
  • $$\dfrac{A^{-1}}{2}$$
  • $$\dfrac{A}{2}$$
  • $$A^{2}$$
Let A=$$\left[ \begin{matrix} 1 \\ 2 \end{matrix}\begin{matrix} 2 \\ 1 \end{matrix} \right] and\quad B=\left[ \begin{matrix} 4 \\ 5 \\ 0 \end{matrix}\begin{matrix} -3 \\ 6 \\ 1 \end{matrix} \right] $$ then
  • $$AB$$ exists
  • $$AB$$ and $$BA$$ both exists
  • Neither $$AB$$ nor $$BA$$ exists
  • $$BA$$ exists, but $$AB$ does not exists
If $$\left[ \begin{matrix} 1 & x & 1 \end{matrix} \right] \left[ \begin{matrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 1 \\ x \end{matrix} \right] =0,$$ then $$x=$$
  • $$\cfrac{-9\pm\sqrt{35}}{2}$$
  • $$\cfrac{-7\pm\sqrt{53}}{2}$$
  • $$\cfrac{-9\pm\sqrt{53}}{2}$$
  • $$\cfrac{-7\pm\sqrt{35}}{2}$$
If $$A$$ and $$B$$ are two matrices such that $$AB$$ and $$A+B$$ are both defined then $$A$$ and $$B$$ are 
  • Square matrices of the same order
  • Square matrices of different order
  • Rectangular matrices of same order
  • Rectangular matrices of different order
if A=$$\left[ \begin{matrix} 2 & 3 \\ 5 & -7 \end{matrix} \right] then\quad \left( { A }^{ '} \right) ^{ 2 }=$$
  • $$\left[ \begin{matrix} 5 & -7 & 12 \\ 1 & 4 & 22 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 1 & 17 \\ 1 & -4 \\ 0 & 2 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} -19 & -25 \\ -15 & 64 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 19 & -25 \\ -15 & 64 \end{matrix} \right] $$
If $$A=\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] $$, then value of $$A^{-1}$$ is equal to 
  • $$A$$
  • $$A^{2}$$
  • $$A^{3}$$
  • $$A^{4}$$
If $$U = [ 2, -3 , 4 ]$$ , $$V = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix}$$ , $$X = [0 , 2 , 3]$$ and $$Y = \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix}$$ , then $$UV + XY$$ =
  • $$20$$
  • $$[ -20 ]$$
  • $$-20$$
  • $$[ 20 ]$$
If $$A=\begin{bmatrix} 2 & -1\\ -7 & 4\end{bmatrix}$$ and $$B=\begin{bmatrix} 4 & 1\\ 7 & 2\end{bmatrix}$$ then $$B^TA^T$$ is equal to?
  • $$\begin{bmatrix} 1 & 0\\ -12 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 1\\ 1 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 0 & 1\\ 1 & 0\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 0\\ 0 & 0\end{bmatrix}$$
Adjacency matrix of all graphs are symmetric.
  • True
  • False
If $$A^2-A+1=0$$, then the inverse of A is?
  • A
  • $$A+I$$
  • $$I-A$$
  • $$A-I$$
If $$\begin{bmatrix} 1 & 1\\ -1 & 1\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}=\begin{bmatrix} 2 \\ 4\end{bmatrix}$$, then the values of $$x $$ and $$y $$ respectively are?
  • $$-3, -1$$
  • $$1, 3$$
  • $$3, 1$$
  • $$-1, 3$$
Let $$\begin{bmatrix} 1 & 1\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 2\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix}.\begin{bmatrix} 1 & n-1\\ 0 & 1\end{bmatrix}=\begin{bmatrix} 1 & 78\\ 0 & 1\end{bmatrix}$$
If $$A=\begin{bmatrix} 1 & n\\ 0 & 1\end{bmatrix}$$ then $$A^{-1}=?$$
  • $$\begin{bmatrix} 1 & 12\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & -13\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & -12\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 0\\ -13 & 1\end{bmatrix}$$
If $$\begin{bmatrix} 1 & 1\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 2\\ 0 & 1\end{bmatrix}\begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix} ..\begin{bmatrix} 1 & n-1\\ 0 & 1\end{bmatrix} =\begin{bmatrix} 1 & 78\\ 0 & 1\end{bmatrix}$$, then the inverse of $$\begin{bmatrix} 1 & n\\ 0 & 1\end{bmatrix}$$ is?
  • $$\begin{bmatrix} 1 & -13\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 0\\ 12 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & -12\\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 0\\ 13 & 1\end{bmatrix}$$
If $$A = \begin{bmatrix} n& 0 & 0\\ 0 & n & 0\\ 0 & 0 & n\end{bmatrix}$$ and $$B = \begin{bmatrix}a_{1} & a_{2} & a_{3}\\ b_{1} & b_{2} & b_{3}\\ c_{1} & c_{2} & c_{3}\end{bmatrix}$$, then $$AB$$ is equal to
  • $$B$$
  • $$nB$$
  • $$B^{n}$$
  • $$A + B$$
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