જો 2X+3Y=left[begin{array}{cc}2 & 3 4 & 0end | vedclass

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Question

(A) આપેલ સમીકરણો છે:$2X+3Y=\left[\begin{array}{cc}2 & 3 \ 4 & 0\end{array}ight]$ ... $(1)$$3X+2Y=\left[\begin{array}{cc}2 & -2 \ -1 & 5\end{array}

Vedclass · Accepted Answer

$X=\left[\begin{array}{cc}\frac{2}{5} & -\frac{12}{5} \ -\frac{11}{5} & 3\end{array}ight], Y=\left[\begin{array}{cc}\frac{2}{5} & \frac{13}{5} \ \frac{14}{5} & -2\end{array}ight]$

Vedclass · Answer

(A) આપેલ સમીકરણો છે:$2X+3Y=\left[\begin{array}{cc}2 & 3 \ 4 & 0\end{array}ight]$ ... $(1)$$3X+2Y=\left[\begin{array}{cc}2 & -2 \ -1 & 5\end{array}ight]$ ... $(2)$સમીકરણ $(1)$ ને $2$ વડે અને સમીકરણ $(2)$ ને $3$ વડે ગુણતા:$4X+6Y=\left[\begin{array}{cc}4 & 6 \ 8 & 0\end{array}ight]$ ... $(3)$$9X+6Y=\left[\begin{array}{cc}6 & -6 \ -3 & 15\end{array}ight]$ ... $(4)$સમીકરણ $(4)$ માંથી $(3)$ બાદ કરતા:$(9X+6Y)-(4X+6Y)=\left[\begin{array}{cc}6 & -6 \ -3 & 15\end{array}ight]-\left[\begin{array}{cc}4 & 6 \ 8 & 0\end{array}ight]$$5X=\left[\begin{array}{cc}2 & -12 \ -11 & 15\end{array}ight] \Rightarrow X=\left[\begin{array}{cc}\frac{2}{5} & -\frac{12}{5} \ -\frac{11}{5} & 3\end{array}ight]$હવે,$X$ ની કિંમત $(1)$ માં મૂકતા:$3Y=\left[\begin{array}{cc}2 & 3 \ 4 & 0\end{array}ight]-2\left[\begin{array}{cc}\frac{2}{5} & -\frac{12}{5} \ -\frac{11}{5} & 3\end{array}ight]$$3Y=\left[\begin{array}{cc}2 & 3 \ 4 & 0\end{array}ight]-\left[\begin{array}{cc}\frac{4}{5} & -\frac{24}{5} \ -\frac{22}{5} & 6\end{array}ight]=\left[\begin{array}{cc}\frac{6}{5} & \frac{39}{5} \ \frac{42}{5} & -6\end{array}ight]$$Y=\left[\begin{array}{cc}\frac{2}{5} & \frac{13}{5} \ \frac{14}{5} & -2\end{array}ight]$

જો $2X+3Y=\left[\begin{array}{cc}2 & 3 \\ 4 & 0\end{array}\right]$ અને $3X+2Y=\left[\begin{array}{cc}2 & -2 \\ -1 & 5\end{array}\right]$ હોય,તો $X$ અને $Y$ શોધો.

Similar Questions

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જો $A = \begin{bmatrix} \sqrt{3} & 1 & -1 \\ 2 & 3 & 0 \end{bmatrix}$ અને $B = \begin{bmatrix} 2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2} \end{bmatrix}$ હોય,તો $A + B = \dots \dots \dots$ શોધો.

જો $A=\left[\begin{array}{ll}6 & 9 \\ 2 & 3\end{array}\right]$ અને $B=\left[\begin{array}{lll}2 & 6 & 0 \\ 7 & 9 & 8\end{array}\right]$ હોય,તો $AB$ શોધો.

$\begin{bmatrix} 7 & 1 & 2 \\ 9 & 2 & 1 \end{bmatrix} \begin{bmatrix} 3 \\ 4 \\ 5 \end{bmatrix} + 2 \begin{bmatrix} 4 \\ 2 \end{bmatrix}$ ની કિંમત શોધો.

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