Filters
Latest Questions
Mathematics
Matrices and determinants
Obtain the inverse of the following matrix using elementary operations $A = \left[ {\begin{array}{*{20}{c}} 0&1&2 \\ 1&2&3 \\ 3&1&1 \end{array}} \right]$

Mathematics
Matrices and determinants
Find x and y, if $x + y = \left[ {\begin{array}{*{20}{c}} 7&0 \\ 2&5 \end{array}} \right]$ and $x - y = \left[ {\begin{array}{*{20}{c}} 3&0 \\ 0&3 \end{array}} \right]$.

Mathematics
Matrices and determinants
Write the value $\left| \begin{matrix} x+y & y+z & z+x \\ z & x & y \\ -3 & -3 & -3 \\ \end{matrix} \right|$

Mathematics
Matrices and determinants
If $A = \left[ {\begin{array}{*{20}{c}} 1&2&2 \\ 2&1&2 \\ 2&2&1 \end{array}} \right]$ , then prove that ${A^2} - 4A - 5I = 0$ , also find ${A^{ - 1}}$ .

Mathematics
Matrices and determinants
If ${A^3} = O$, then $I + A + {A^2}$ equals
A.$I - A$
B.$\left( {I + {A^{ - 1}}} \right)$
C.${\left( {I - A} \right)^{ - 1}}$
D.None of these

Mathematics
Matrices and determinants
Write the value of x if \left|\begin{align} & 2x\text{ 5} \\ & \text{8 x} \\ \end{align} \right| =\left|\begin{align} & \text{6 -2} \\ & \text{7 3} \\ \end{align} \right| .
Mathematics
Matrices and determinants
Without expanding the determinant, prove that $\left. \left| \begin{matrix} a & {{a}^{2}} & bc \\ b & {{b}^{2}} & ca \\ c & {{c}^{2}} & ab \\ \end{matrix} \right. \right|=\left. \left| \begin{matrix} 1 & {{a}^{2}} & {{a}^{3}} \\ 1 & {{b}^{2}} & {{b}^{3}} \\ 1 & {{c}^{2}} & {{c}^{3}} \\ \end{matrix} \right. \right|$.
Mathematics
Matrices and determinants
If $\alpha ,\beta \text{ and }\gamma$ are the roots of the equation ${{x}^{3}}+px+q=0$ then the value of determinant $\left| \begin{matrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{matrix} \right|$ is
\begin{align} & A.p \\ & B.q \\ & C.{{p}^{2}}-2q \\ & D.0 \\ \end{align}

Mathematics
Matrices and determinants
Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if 
A. The first column of M is the transpose of the second row of M
B. The second row of M is the transpose of the first column of M 
C. M is a diagonal matrix with non-zero entries in the main diagonal
D. The product of entries in the main diagonal of M is not the square of an integer
Mathematics
Matrices and determinants
Using properties of determinants, show that $\left| \begin{matrix} a+b & a & b \\ a & a+c & c \\ b & c & b+c \\ \end{matrix} \right|=4abc$

Mathematics
Matrices and determinants
If $\alpha$ , $\beta \ne 0$ , and $f\left( n \right) = {\alpha ^n} + {\beta ^n}$ and $\left| {\begin{array}{*{20}{c}} 3&{1 + f\left( 1 \right)}&{1 + f\left( 2 \right)} \\ {1 + f\left( 1 \right)}&{1 + f\left( 2 \right)}&{1 + f\left( 3 \right)} \\ {1 + f\left( 2 \right)}&{1 + f\left( 3 \right)}&{1 + f\left( 4 \right)} \end{array}} \right| = K{\left( {1 - \alpha } \right)^2}{\left( {1 - \beta } \right)^2}{\left( {\alpha - \beta } \right)^2}$ , then K is equal to
A $\alpha \beta$
B $\dfrac{1}{{\alpha \beta }}$
C 1
D -1

Mathematics
Matrices and determinants
If $A$ and $B$ are square matrices of order $3$ such that $\left| A \right|=-1$, $\left| B \right|=3$, then $\left| 3AB \right|$ is equal to
A. $-9$
B. $-81$
C. $-27$
D. 81
Prev
1
2
3
4
5