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CBSE Questions for Class 12 Commerce Maths Matrices Quiz 8 - MCQExams.com

If A is a scalar matrix kI with scalar k0 of order 3, the A1 is:
  • 1k2I
  • 1k3I
  • 1kI
  • kI
If A=[7213] and A+B=[1024], then matrix B=?
  • [1011]
  • [6231]
  • [8217]
  • [8217]
If A=[4263], then A2 is
  • [164369]
  • [84126]
  • [4263]
  • [4263]
If A+B=[2345] and A=[1203], then matrix B is
  • [1142]
  • [1412]
  • [2411]
  • [4211]
If \bigl(\begin{smallmatrix} 1& 2\\ 2 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} x \\ y \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 2 \\  4 \end{smallmatrix}\bigr), then the values of x and y respectively, are
  • 2, 0
  • 0, 2
  • 0, -2
  • 1, 1
If \begin{bmatrix} 5 & x & 1 \end{bmatrix} \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}  = (20), then the value of x is
  • 7
  • -7
  • \dfrac{1}{7}
  • 0
If A = \begin{bmatrix}7 &2 \\ 1 & 3\end{bmatrix} and A + B = \begin{bmatrix} -1& 0\\ 2 & -4\end{bmatrix}, then the matrix B =
  • \left[\begin{matrix}1 &0 \\ 0 & 1\end{matrix}\right]
  • \left[\begin{matrix} 6&2 \\ 3 & -1\end{matrix}\right]
  • \left[\begin{matrix} -8& -2\\ 1 & -7\end{matrix}\right]
  • \left[\begin{matrix} 8& 2\\ -1 & 7\end{matrix}\right]
Choose the correct statement related to the matrices A=\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix} and B=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
  • A^3=A, B^3 \ne B
  • A^3\ne A, B^3=B
  • A^3=A, B^3 = B
  • A^3\ne A, B^3 \ne B
If A = \bigl(\begin{smallmatrix} 4& -2\\ 6 & -3\end{smallmatrix}\bigr), then A^2 is
  • \bigl(\begin{smallmatrix} 16 & 4\\ 36 & 9\end{smallmatrix}\bigr)
  • \bigl(\begin{smallmatrix}8 & -4\\ 12 & -6\end{smallmatrix}\bigr)
  • \bigl(\begin{smallmatrix} -4& 2\\ -6 & 3\end{smallmatrix}\bigr)
  • \bigl(\begin{smallmatrix} 4& -2\\ 6 & -3\end{smallmatrix}\bigr)
\bigl(\begin{smallmatrix} -1& 0\\ 0 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix}a & b\\ c & d\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 1& 0\\ 0 & -1\end{smallmatrix}\bigr), then the values of a, b, c and d respectively are
  • -1, 0, 0, -1
  • 1, 0, 0, 1
  • -1, 0, 1, 0
  • 1, 0, 0, 0
If \bigl(\begin{smallmatrix}a & 3\\ 1 & 2\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} 2 \\ -1 \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 5\\ 0 \end{smallmatrix}\bigr), then the value of a is
  • 8
  • 4
  • 2
  • 11
If A=\left[ \begin{matrix} 1 & -2 & 3 \end{matrix} \right] and B=\left[ \begin{matrix} -1 \\ 2 \\ -3 \end{matrix} \right] , then A + B is
  • \begin{bmatrix} 0& 0 & 0 \end{bmatrix}
  • \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}
  • \begin{bmatrix} -1& 4 \end{bmatrix}
  • not defined
If matrix A=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix} such that Ax=I, then x=................
  • \cfrac { 1 }{ 5 } \begin{bmatrix} 1 & 3 \\ 2 & -1 \end{bmatrix}
  • \cfrac { 1 }{ 5 } \begin{bmatrix} 4 & 2 \\ 4 & -1 \end{bmatrix}
  • \cfrac { 1 }{ 5 } \begin{bmatrix} -3 & 2 \\ 4 & -1 \end{bmatrix}
  • \cfrac { 1 }{ 5 } \begin{bmatrix} -1 & 2 \\ -1 & 4 \end{bmatrix}
The matrix A = \begin{bmatrix} 0& 1 & -1\\ -1 & 0 & 1\\ 1 & -1 & 0\end{bmatrix} is a :
  • Diagonal matrix
  • Symmetric matrix
  • Skew-symmetric matrix
  • Identity matrix
The inverse of a diagonal matrix is a :
  • Symmetric matrix
  • Skew-symmetric matrix
  • Diagonal matrix
  • None of the above
If \begin{bmatrix} 3 & -1 \\ 0 & 6 \end{bmatrix}\begin{bmatrix} 3x \\ 1 \end{bmatrix}+\begin{bmatrix} -2x \\ 3 \end{bmatrix}=\begin{bmatrix} 8 \\ 9 \end{bmatrix}, then the value of x is
  • -\dfrac { 3 }{ 8 }
  • 7
  • -\dfrac { 2 }{ 9 }
  • None of these
Let A = \begin{bmatrix}x + y & y\\ 2x & x - y\end{bmatrix}, B = \begin{bmatrix} 2& -1\end{bmatrix} and C = \begin{bmatrix} 3& 2\end{bmatrix}. If AB = C, then A^{2} is equal to
  • \begin{bmatrix} 6 & -10\\ 4 & 26 \end{bmatrix}
  • \begin{bmatrix} -10 & 5\\ 4 & 24 \end{bmatrix}
  • \begin{bmatrix} -5 & -6\\ -4 & -20 \end{bmatrix}
  • None of these.
If the matrix A is such that \begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix} A=\begin{bmatrix} 1 & 1 \\ 0 & -1\end{bmatrix}, then what is equal to A?
  • \begin{bmatrix} 1 & 4 \\ 0 & -1\end{bmatrix}
  • \begin{bmatrix} 1 & 4 \\ 0 & 1\end{bmatrix}
  • \begin{bmatrix} -1 & 4\\ 0 & -1\end{bmatrix}
  • \begin{bmatrix} 1 & -4 \\ 0 & -1\end{bmatrix}
If A=\begin{bmatrix}1&1&-1\\2&-3&4\\3&-2&3\end{bmatrix} and B=\begin{bmatrix}-1&-2&-1\\6&12&6\\5&10&5\end{bmatrix}, then which of the following is/are correct?
A and B commute.
AB is null matrix.
Select the correct answer using the code given below :
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
If \begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix}\times \begin{pmatrix} 5 & -2 \\ -3 & 1 \end{pmatrix}=\begin{pmatrix} 1 & -1 \\ 17 & \lambda  \end{pmatrix} then what is \lambda equal to?
  • 7
  • -7
  • 9
  • -9
If \quad A=\begin{pmatrix} 1 & 3 \\ 4 & 5 \end{pmatrix} then { A }^{ -1 } equals
  • \cfrac { 1 }{ 7 } \left( A+6I \right)
  • \cfrac { 1 }{ 7 } \left( A-6I \right)
  • \cfrac { 1 }{ 7 } \left( 6I-A \right)
  • None of these
If [1\,x\,1]  \begin{bmatrix} 1&3&2 \\ 0&5&1\\0&2&0 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0, then the values of x are:
  • 1,5
  • -1,-5
  • 1,6
  • -1,-6
  • 3,3
If A = \begin{bmatrix} 2& 3\\ -1 & 2\end{bmatrix}, then A^{3} + 3A^{2} - 4A + 1 is equal to
  • \begin{bmatrix} 1& 1\\ 1 & 0\end{bmatrix}
  • \begin{bmatrix} -14& 51\\ -17 & -14\end{bmatrix}
  • \begin{bmatrix} -14& -51\\ -17 & -14\end{bmatrix}
  • \begin{bmatrix} -1& -1\\ -1 & 0\end{bmatrix}
If A=\begin{pmatrix} 3 & 1 \\ -9 & -3 \end{pmatrix} then { \left( 1+2A+3{ A }^{ 2 }+....\infty  \right)  }^{ -1 } equals
  • \begin{pmatrix} -5 & -2 \\ 18 & 7 \end{pmatrix}
  • \begin{pmatrix} -5 & 18 \\ -2 & 7 \end{pmatrix}
  • \begin{pmatrix} 7 & -2 \\ 18 & -5 \end{pmatrix}
  • None of these
If \begin{bmatrix} \alpha  & \beta  \\ \gamma  & -\alpha  \end{bmatrix} to the square is two rowed unit matrix, then \alpha ,\beta ,\gamma should satisfy the relation
  • 1+{ \alpha }^{ 2 }+\beta \gamma =0
  • 1-{ \alpha }^{ 2 }-\beta \gamma =0
  • 1-{ \alpha }^{ 2 }+\beta \gamma =0
  • { \alpha }^{ 2 }+\beta \gamma -1=0
If A=\begin{bmatrix} \alpha  & 0 \\ 1 & 1 \end{bmatrix} and B=\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}, then value of \alpha for which {A}^{2}=B, is
  • 1
  • -1
  • 4
  • No real value
If A = \begin{bmatrix}1 &3 \\ 3 & 4\end{bmatrix} and A^{2} - kA - 5I_{2} = 0, then the value of k is
  • 3
  • 5
  • 7
  • -7
If A=\begin{bmatrix} 1 & -3 \\ 2 & k \end{bmatrix} and { A }^{ 2 }-4A+10I=A, then k is equal to
  • 0
  • -4
  • 4 and not 1
  • 1 or 4
If A = \begin{vmatrix} 5 & x-2 \\ 2x+3 & x+1 \end{vmatrix} is symmetric, then x = _____
  • 4
  • 5
  • -5
  • -4
If A is a non zero square matrix of order n with det\left( I+A \right) \neq 0, and {A}^{3}=0, where I,O are unit and null matrices of order n\times n respectively, then { \left( I+A \right)  }^{ -1 }=
  • I-A+{ A }^{ 2 }
  • I+A+{ A }^{ 2 }
  • I+{ A }^{ 2 }
  • I+A
0:0:1


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