Math, asked by adhithya793, 9 months ago

please say the answer....​

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Answered by VishnuPriya2801
28

Question:-

Find x , y , z and w if  \\\begin{bmatrix} \sf x - y & \sf2x + z \\\\\sf2x - y & \sf3z + w \end{bmatrix} = \begin{bmatrix}  \sf - 1 & \sf5 \\\\\sf0&\sf13\end{bmatrix}\quad

Answer:-

Given:

 \: \begin{bmatrix} \sf{ x - y} &  \sf{2x + z  }\\  \\  \sf{2x - y} & \sf 3z + w \end{bmatrix} = \begin{bmatrix}  \sf- 1 &  \sf5  \\ \\ \sf  0& \sf13\end{bmatrix} \quad

On comparing both sides we get,

  • x - y = - 1 -- equation (1)

  • 2x - y = 0 -- equation (2)

  • 2x + z = 5 -- equation (3)

  • 3z + w = 13 -- equation (4)

Subtract equation (1) from (2).

→ 2x - y - (x - y) = 0 - ( - 1)

→ 2x - y - x + y = 1

→ x = 1

Substitute x value in equation (1).

→ 1 - y = - 1

→ 1 + 1 = y

→ 2 = y

Substitute x value in equation (3).

→ 2 * 1 + z = 5

→ z = 5 - 2

→ z = 3

Substitute z value in equation (4).

→ 3 * 3 + w = 13

→ w = 13 - 9

→ w = 4

Therefore,

  • x = 1

  • y = 2

  • z = 3

  • w = 4
Answered by tarracharan
2

{\boxed{\sf{x=1}}}

{\boxed{\sf{y=2}}}

{\boxed{\sf{z=3}}}

{\boxed{\sf{w=4}}}

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