`If [[X,3x- Y],[2x+Z,3y -w ]]=[[3,2],[4,7]]` Find X,Y,Z,W - Mathematics

प्रश्न

$I f [\begin{matrix} x & 3 x - y \\ 2 x + z & 3 y - w \end{matrix}] = [\begin{matrix} 3 & 2 \\ 4 & 7 \end{matrix}]$ find x,y,z,w

उत्तर

Since all the corresponding elements of a matrix are equal,

$[\begin{matrix} x 3 x - y \\ 2 x + z 3 y - w \end{matrix}] = [\begin{matrix} 3 2 \\ 4 7 \end{matrix}]$

x=3 ...(1)

3x−y=2 ...(2)

Putting the value of x in eq. (2), we get

3(3)−y=2

⇒9−y=2

⇒−y=−7

⇒ y=7

2x+z=4 ...(3)

Putting the value of x in eq. (3), we get

2(3)+z=4

⇒6+z=4

⇒z=4−6

⇒z=−2

3y−w=7 ...(4)

Putting the value of y in eq. (4), we get

3(7)−w=7

⇒21−w=7

⇒21−7=w

⇒w=14

∴ x=3 , y=7, z=−2 and w=14

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Equality of Matrices

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Q 12 Q 11 Q 13

पाठ 5: Algebra of Matrices - Exercise 5.1 [पृष्ठ ७]

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पाठ 5 Algebra of Matrices
Exercise 5.1 | Q 12 | पृष्ठ ७

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Equality of Matrices

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$I f [\begin{matrix} X & 3 x - Y \\ 2 x + Z & 3 y - w \end{matrix}] = [\begin{matrix} 3 & 2 \\ 4 & 7 \end{matrix}]$ Find X,Y,Z,W - Mathematics

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