Find the values of x and y if : \(\begin{bmatrix} x+10& y^2+2y \\[0.3

1.	Find the values of x and y if : \(\begin{bmatrix} x+10& y^2+2y \\[0.3em] 0 & -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&3 \\[0.3em] 0 & y^2-5y \\[0.3em] \end{bmatrix} \)
Answer» Given two matrices are equal. i.e, A = B. \(\begin{bmatrix} x+10& y^2+2y \\[0.3em] 0 & -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&3 \\[0.3em] 0 & y^2-5y \\[0.3em] \end{bmatrix} \) We know that if two matrices are equal then the elements of each matrices are also equal. ∴ x + 10 = 3x + 4 ⇒ x – 3x = 4 – 10 ⇒ – 2x = – 6 ⇒ x = 3 …(1) And y²+ 2y = 3 ⇒ y² + 2y – 3 = 0 ⇒ y² + 3y – y – 3 = 0 ⇒ y(y + 3) – 1(y + 3) = 0 ⇒ (y + 3)(y – 1) = 0 ⇒ y = – 3 or 1 …(2) And y² – 5y = – 4 ⇒ y² – 5y + 4 = 0 ⇒ y² – 4y – y + 4 = 0 ⇒ y(y – 4) – 1(y – 4) = 0 ⇒ (y – 4)(y – 1) = 0 ⇒ y = 4 or 1 …(3) ∴ The common value is x = 3 and y = 1

Find the values of x and y if : \(\begin{bmatrix} x+10& y^2+2y \\[0.3em] 0 & -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&3 \\[0.3em] 0 & y^2-5y \\[0.3em] \end{bmatrix} \)

Answer»

Given two matrices are equal.

i.e, A = B.

\(\begin{bmatrix} x+10& y^2+2y \\[0.3em] 0 & -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&3 \\[0.3em] 0 & y^2-5y \\[0.3em] \end{bmatrix} \)

We know that if two matrices are equal then the elements of each matrices are also equal.

∴ x + 10 = 3x + 4

⇒ x – 3x = 4 – 10

⇒ – 2x = – 6 ⇒ x = 3 …(1)

And y²+ 2y = 3

⇒ y² + 2y – 3 = 0

⇒ y² + 3y – y – 3 = 0

⇒ y(y + 3) – 1(y + 3) = 0

⇒ (y + 3)(y – 1) = 0

⇒ y = – 3 or 1 …(2)

And y² – 5y = – 4

⇒ y² – 5y + 4 = 0

⇒ y² – 4y – y + 4 = 0

⇒ y(y – 4) – 1(y – 4) = 0

⇒ (y – 4)(y – 1) = 0

⇒ y = 4 or 1 …(3)

∴ The common value is x = 3 and y = 1

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Find the values of x and y if : \(\begin{bmatrix} x+10&amp; y^2+2y \\[0.3em] 0 &amp; -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&amp;3 \\[0.3em] 0 &amp; y^2-5y \\[0.3em] \end{bmatrix} ​​\)

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Find the values of x and y if : \(\begin{bmatrix} x+10& y^2+2y \\[0.3em] 0 & -4 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 3x+4&3 \\[0.3em] 0 & y^2-5y \\[0.3em] \end{bmatrix} \)