If \(AB=I\) and \(AC=I\) then what about \(B\) and \(C\)
If \(AB=A\) and \(BA=B\) then \(B^2=\)?
If \(A\) is symmetric matrix then \(A^t\) is
$$ X+2I = \begin{bmatrix} 5 & 7 & 8 \ 9 & 2 & 1 \ 0 & 2 & 3 \end{bmatrix} $$ then \(X=\)?
If \(A=[a_{ij}]_{3\times 4}\) \(B=[b_{ij}]_{4\times 3}\) then which of the follwoing is true? </p><div><div class="md-radio "><input id="5-0" type="radio" name="5"><label for="5-0">\)\lambda A+\lambda B=\lambda(A+B)\)
$$ \begin{vmatrix} 1 & 2 & 4 \ 8 & 16 & 32 \ 64 & 128 & 256 \end{vmatrix}= \(\(? </p><div><div class="md-radio "><input id="6-0" type="radio" name="6"><label for="6-0">\)1028\)
If $$ \begin{bmatrix} \alpha & 2 \ 2 & \alpha \end{bmatrix} $$ and \(|A|^3=125\) then \(\alpha=\)?
If $$ \begin{cases} a_{11}x_1+a_{12}x_2+a_{13}x_3=b_1 \ a_{21}x_1+a_{22}x_2+a_{23}x_3=b_2 \ a_{31}x_1+a_{32}x_2+a_{33}x_3=b_3 \end{cases} $$ be a non=homogenous system and \(|A|\not = 0\) then which is true?
$$ \begin{vmatrix} a & b & c \ d & e & f \ g & h & i \end{vmatrix}=3 $$ then $$ \begin{vmatrix} 2a & 2b & 2c \ 2d & 2e & 2f \ 2g & 2h & 2i \end{vmatrix}= \(\(? </p><div><div class="md-radio "><input id="10-0" type="radio" name="10"><label for="10-0">\)3\)
$$ \begin{bmatrix} p & o & o \ o & p & o \end{bmatrix} $$ is called _______ matrix?
The order of $$ \begin{bmatrix} p & q & r \end{bmatrix} \begin{bmatrix} a & b & c \ d & e & t \ g & h & i \end{bmatrix} \begin{bmatrix} l & o \ m & p\ n & q \end{bmatrix} $$ is
If $$ \begin{vmatrix} a & b & c \ d & e & f\ g & h & i \end{vmatrix} = 7 $$ then $$ \begin{vmatrix} a+d & b+e & c+f \ d & e & f\ g & h & i \end{vmatrix} = \(\(? </p><div><div class="md-radio "><input id="13-0" type="radio" name="13"><label for="13-0">\)7\)
The matrix $$ \begin{bmatrix} 0 & 8 & 9 \ -8 & 0 & 15\ -9 & -15 & 0 \end{bmatrix} $$ is known as
The equations \(x+4y-2z=3\), \(3x+y+5z=7\), \(2x+3y+2z=5\) have
$$ \begin{vmatrix} 1 & 0 & 0 & 0\ 5 & 7 & 0 & 0\ 3 & 0 & 5 & 0\ 9 & 0 & 0 & 2 \end{vmatrix}= \((?
If \(A\) is \(3\times4\) matrix, \(B\) is a matrix such that \(AB\) and \(BA\) both are defined then order of matrix \(B\) is? </p><div><div class="md-radio "><input id="17-0" type="radio" name="17"><label for="17-0">\)3\times4\)
The equations \(x+2y+3z=0\), \(x-y+4z=0\) and \(2x+y+7z=0\) have
The transpose operation on matrices statisfies the following properties except
If \(A\) and \(B\) are square matrices of same order such that \((A+B)^2= A^2 + 2AB + B^2\) Then
If $$ \begin{bmatrix} 1 & a\ \end{bmatrix}\begin{bmatrix} 1 & 3\ 0 & 5 \end{bmatrix}\begin{bmatrix} a\ 1 \end{bmatrix} =0$$ then \(a\) is?
If $$ A= \begin{bmatrix} 2 & 3 \ 1 & 1 \ 5 & 6 \end{bmatrix} $$, $$ B= \begin{bmatrix} 3 & 2 \ 5 & 7 \ 2 & 1 \end{bmatrix} $$ and \(A+B-C=0\) then \(C=\)?
If \(A\) and \(B\) are two matrices such that \(A + B\) and \(AB\) are defined then. </p><div><div class="md-radio "><input id="23-0" type="radio" name="23"><label for="23-0">\)A\) and \(B\) are two matrices not necessarily of same order
If $$ \begin{bmatrix} 4 & 3 \ 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & y \ x & -1 \end{bmatrix} = \begin{bmatrix} 4 & 5 \ 2 & 3 \end{bmatrix} $$ then \(x+y=\)?
If the matrix \(AB\) is zero then
What is called a matrix of order \(m\times1\)
If \(A\) and \(B\) are two square matrices of same order. Then \((A+B)^2 =\)?
If \(A,B,C\) are three matrices such that $AB = AC \implies B = C $ then A is
If A and B are non-singular matrices Then \((AB)^{-1}=\)
Minors and co–factors of the elements in a determinant are in equal magnitude but they may differ in
If each element of a \(3\times3\) matrix \(A\) is multiplied by \(3\) then the determinant of the resulting matrix is?
The system of equations \(x+2y=5\) and \(-3x-6y=15\) has
For homogenous linear equations, system \(AX=0\) has non-trivial solution if \(|A|=\)
If a matrix \(A\) with real entries then \(overline{A}=\)
Which matrix can be rectangular matrix?
If $$ A = \begin{bmatrix} 1 & 0 & -1 & 2 \ 3 & 1 & 2 & 5 \ 0 & -2 & 1 & 6 \end{bmatrix} $$, $$ A = \begin{bmatrix} 2 & -1 & 3 & 1 \ 1 & 3 & -1 & 4 \ 3 & 1 & 2 & -1 \end{bmatrix} $$ then \((2,3)\)rd element of \((A+B)^t\) is
If \(A=[a_{ij}]_{m\times n}\), \(B=[b_{ij}]_{n\times r}\) then order of \((AB)^t\) is
Which one is not symmetric?
\(AB\) is symmetric if
The co factor of an element \(a_{ij}\) denoted by \(A_{ij}\) is?
$$ B = \begin{bmatrix} 0 & -4 & 1 \ 4 & 0 & -3 \ -1 & 3 & 0 \end{bmatrix} $$ then
If $$ \Delta = \begin{bmatrix} c & a & x \ m & m & m \ b & x & b \end{bmatrix} $$ then the roots of \(\Delta=0\) are given by
If \(x=-9\) is root of $$ \begin{vmatrix} x & 3 & 7 \ 2 & x & 2 \ 7 & 6 & x \end{vmatrix} =0 $$ then the other two roots are
If $$ A\cdotp \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 5 & 3 \ 2 & -3 \end{bmatrix} $$ then matrix \(A\) is
If $$ P = \begin{bmatrix} 3 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 3 \end{bmatrix} $$ then \(P^4\)
The system \(3a + 5b = 6\), \(9a + 15b = 12\) has __________ Solution
If $$ A = \begin{bmatrix} 4 & 2 \ 0 & 3 \end{bmatrix} $$, $$ B = \begin{bmatrix} \frac{1}{4} & s \ 0 & \frac{1}{3} \end{bmatrix} $$ then value of \(s\) such that \(AB=I\) is
If \(a_1x + b_1y + c_1z = d_1\), \(a_2x + b_2y + c_2z = d_2\), \(a_3x + b_3y +c_3z = d_3\) Then \(z=\)
If $$ \begin{vmatrix} l & m & n \ o & p & q \ r & s & t \end{vmatrix} = 30 $$ then $$ \begin{vmatrix} l & o & r \ m & p & s \ n & q & t \end{vmatrix} $$
If If \(a\), \(b\), \(c\) are positive real numbers other than one and \(a = b = c\) then $$ \begin{vmatrix} \log_ab & \log_ac & 1 \ \log_bc & \log_ba & 1 \ 1 & \log_ca & \log_cb \ \end{vmatrix} $$