Matrix

Algebra Level 1

If [ 2 x y 5 3 y ] = [ 8 5 3 6 ] , \begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 8 & 5 \\ 3 & 6 \end{bmatrix}, then what is the value of 12 x ? 12x?


The answer is 84.

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3 solutions

Nazmus Sakib
Sep 23, 2017

[ 2 x y 5 3 y ] = [ 8 5 3 6 ] , \begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 8 & 5 \\ 3 & 6 \end{bmatrix},

here, 2 x y = 8 2x-y=8 ....(i) and y = 6 y=6 ..........(ii)

so, 2 x 6 = 8 2x-6=8

or, 2 x = 14 2x=14

or, x = 7 x=7

or, 12 x = 12 × 7 12x= 12\times 7

or, 12 x = 84 12x= \large\boxed{84}

Mohammad Khaza
Sep 26, 2017

[ 2 x y 5 3 y ] = [ 8 5 3 6 ] \begin{bmatrix}2x-y & 5 \\3 & y \end{bmatrix}=\begin{bmatrix} 8 & 5 \\ 3 & 6 \end{bmatrix}

we get, 2 x y = 8 2x-y=8 .....................[1]

and y = 6 y=6 ................................[2]

by doing [1]+[2], we get,

2 x y + y = 8 + 6 2x-y+y=8+6

or, x = 7 x=7

or, 12 x = 7 × 12 = 84 12x=7 \times 12=84

Hana Wehbi
Sep 21, 2017

[ 2 x y 5 3 y ] = [ 8 5 3 6 ] , \begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 8 & 5 \\ 3 & 6 \end{bmatrix},

then 2 x y = 8 2x-y = 8 and y = 6 y=6 ;

Solving for x x by plugging in y x = 7 12 x = 12 × 7 = 84 y \implies x=7 \implies 12x= 12\times 7 = 84

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