જો A = left[ {begin{array}{*{20}{c}}1&02&0end{array}} right],B = left[ {begin{array}{*{2

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3 and 4 .Determinants and Matrices

easy

જો $A = \left[ {\begin{array}{{20}{c}}1&0\\2&0\end{array}} \right],B = \left[ {\begin{array}{{20}{c}}0&0\\1&{12}\end{array}} \right]$, તો

$AB = O,BA = O$

$AB = O,BA \ne O$

$AB \ne O,BA = O$

$AB \ne O,BA \ne O$

Solution

(b) $AB = \,\left[ {\begin{array}{*{20}{c}}1&0\\2&0\end{array}\,} \right]\,\left[ {\begin{array}{*{20}{c}}0&0\\1&{12}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0\\0&0\end{array}} \right] = O$

while $BA = \left[ {\begin{array}{*{20}{c}}0&0\\1&{12}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&0\\2&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0\\{25}&0\end{array}} \right]\, \ne O$.

Standard 12

Mathematics

$A$ અને $B$ એ $3 \times 3$ કક્ષાનો શ્રેણિક છે કે જેથી $AB + A + B = 0$ હોય તો . . . .

normal

$x$ ની કઈ કિંમત માટે $:\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=\mathrm{O} ?$

medium

શ્રેણિક$AB = O$ નો ગુણાકાર હોય તો . . .

normal

જો $\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right],$ હોય, તો સાબિત કરો કે $A^{3}-6 A^{2}+7 A+2 I=0$

hard

જો $A=\left[\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right],$ અને $C=\left[\begin{array}{ccc}4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -2 & 3\end{array}\right],$ હોય, તો $(A+B)$ અને $(B-C)$ ની ગણતરી કરો. વળી, ચકાસો કે $A+(B-C)=(A+B)-C$