જો X+Y=left[begin{array}{ll}5 & 2 0 &amp | vedclass

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(A) આપેલ સમીકરણો:
$X + Y = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight]$ --- $(1)$
$X - Y = \left[\begin{array}{cc}3 & 6 \ 0

Vedclass · Accepted Answer

$X=\left[\begin{array}{ll}4 & 4 \ 0 & 4\end{array}ight]$,$Y=\left[\begin{array}{rr}1 & -2 \ 0 & 5\end{array}ight]$

Vedclass · Answer

(A) આપેલ સમીકરણો:
$X + Y = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight]$ --- $(1)$
$X - Y = \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$ --- $(2)$
સમીકરણ $(1)$ અને $(2)$ નો સરવાળો કરતા:
$(X + Y) + (X - Y) = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight] + \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$
$2X = \left[\begin{array}{ll}5+3 & 2+6 \ 0+0 & 9-1\end{array}ight] = \left[\begin{array}{ll}8 & 8 \ 0 & 8\end{array}ight]$
$X = \frac{1}{2} \left[\begin{array}{ll}8 & 8 \ 0 & 8\end{array}ight] = \left[\begin{array}{ll}4 & 4 \ 0 & 4\end{array}ight]$
સમીકરણ $(1)$ માંથી $(2)$ બાદ કરતા:
$(X + Y) - (X - Y) = \left[\begin{array}{ll}5 & 2 \ 0 & 9\end{array}ight] - \left[\begin{array}{cc}3 & 6 \ 0 & -1\end{array}ight]$
$2Y = \left[\begin{array}{ll}5-3 & 2-6 \ 0-0 & 9-(-1)\end{array}ight] = \left[\begin{array}{ll}2 & -4 \ 0 & 10\end{array}ight]$
$Y = \frac{1}{2} \left[\begin{array}{ll}2 & -4 \ 0 & 10\end{array}ight] = \left[\begin{array}{ll}1 & -2 \ 0 & 5\end{array}ight]$

જો $X+Y=\left[\begin{array}{ll}5 & 2 \\ 0 & 9\end{array}\right]$ અને $X-Y=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]$ હોય,તો $X$ અને $Y$ શોધો.

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જો $A = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix}$ અને $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$ હોય,તો:

ધારો કે $n \geq 2$ એક પૂર્ણાંક છે. $A = \begin{bmatrix} \cos (2 \pi / n) & \sin (2 \pi / n) & 0 \\ -\sin (2 \pi / n) & \cos (2 \pi / n) & 0 \\ 0 & 0 & 1 \end{bmatrix}$ અને $I$ એ $3$ કક્ષાનો એકમ શ્રેણિક છે. તો,

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