Let A=left[begin{array}{ll}2 & 4 3 & 2end{array}right], B=left[begin{array}{cc}1 & 3 -2

Hindi

3 and 4 .Determinants and Matrices

easy

Let $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

Find $3A-C$

$\left[\begin{array}{ll}8 & 7 \\ 6 & 2\end{array}\right]$

Solution

$3 A-C=3\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]-\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

$=\left[\begin{array}{ll}3 \times 2 & 3 \times 4 \\ 3 \times 3 & 3 \times 2\end{array}\right]-\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

$=\left[\begin{array}{cc}6 & 12 \\ 9 & 6\end{array}\right]-\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

$=\left[\begin{array}{ll}6+2 & 12-5 \\ 9-3 & 6-4\end{array}\right]$

$=\left[\begin{array}{ll}8 & 7 \\ 6 & 2\end{array}\right]$

Standard 12

Mathematics

Let $2A+B = \left[ {\begin{array}{{20}{c}}
1&0&3 \\
{ – 1}&4&6 \\
2&5&2
\end{array}} \right],\,A – 2B = \left[ {\begin{array}{{20}{c}}
2&{ – 1}&5 \\
0&3&6 \\
1&2&1
\end{array}} \right]$ . Then $Tr(A) -Tr(B)$ has the value equal to (where $Tr(A)$ denotes the trace of matrix $A$)

normal

If $A =$ $\left( {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right)$ satisfies the equation $x^2 – (a + d) x + k = 0$, then

medium

Which one of the following is not true

normal

$A,B$ are n-rowed square matrices such that $AB = O$ and $B$ is non-singular. Then

normal

If $\left[\begin{array}{ccc}x+3 & z+4 & 2 y-7 \\ -6 & a-1 & 0 \\ b-3 & -21 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & 6 & 3 y-2 \\ -6 & -3 & 2 c+2 \\ 2 b+4 & -21 & 0\end{array}\right]$ then find the values of $a,\, b, \,c, \,x, \,y$ and $z$.

medium