Classes
Class 9Class 10First YearSecond Year
Example.Let A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & 6 & 8 \\ -1 & 2 & -3\end{array}\right] and B=\left[\begin{array}{ccc}2 & 3 & 4 \\ -4 & 6 & -8 \\ 1 & 2 & 5\end{array}\right] Then(iii)\begin{aligned}A B &=\left[\begin{array}{ccc}2-8+3 & 3+12+6 & 4-16+15 \\8-24+8 & 12+36+16 & 16-48+40 \\-2-8-3 & -3+12-6 & -4-16-15\end{array}\right] \\&=\left[\begin{array}{ccc}-3 & 21 & 3 \\-8 & 64 & 8 \\-13 & 3 & -35\end{array}\right]\end{aligned}

$Q.20 If A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] then adj A equals :(a) \left[\begin{array}{rr}d & b \\ -c & a\end{array}\right] (b) \left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right] (c) \left[\begin{array}{ll}d & b \\ c & a\end{array}\right] (d) \left[\begin{array}{rr}d & -b \\ c & a\end{array}\right] Gujranwala Board 2007$

$Evaluate the following determinants using their properties.8. \left|\begin{array}{lll}x & y & z \\ z & x & y \\ y & z & x\end{array}\right|$

$Evaluate the following determinants:6. \left|\begin{array}{lll}1 & 1 & \omega \\ 1 & 1 & \omega^{2} \\ \omega & \omega^{2} & 1\end{array}\right| where \omega is a complex cube root of unity.$

$17. Let \mathrm{A}=\left[\begin{array}{ccc}1 & 3 & 0 \\ -1 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \mathrm{B}=\left[\begin{array}{ccc}2 & 3 & 4 \\ 1 & 2 & 3 \\ -1 & 1 & 2\end{array}\right] and C=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 5 & 8 \\ 2 & 7 & 6\end{array}\right] Show that :(V) \mathrm{A}+\mathrm{B}=\mathrm{B}+\mathrm{A}^{-7}=\pm=$

$(vi) Product of \left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right] is(a) [2 x+y] (b) [x-2 y] (c) [2 x-y] (d) [x+2 y]$

$Q.14 \left[\begin{array}{lll}0 & 0 & 0\end{array}\right] is(a) scalar matrix(b) diagonal matrix(c) identity matrix(d) null matrix$