If P - begin bmatrix 1 - 2 13 - 4y Xend bmatrix - then PX - begin bmatrix 4115end bmatrix - Find the value of y -A- -3

The correct option is A 3Given, P = [ 1 amp; 2; nbsp; 3 amp; 4 ] nbsp; X = [ y; nbsp; x ] PX = [ 4; nbsp; 5 ] ∴ nbsp;[ 1 amp; 2 ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Matrices

If P = begin ...

Question

If $P = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $X = [\begin{matrix} y x \end{matrix}]$ , then $P X = [\begin{matrix} 45 \end{matrix}]$ . Find the value of y?
-3

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Solution

The correct option is A -3
Given,
$P = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$
$X = [\begin{matrix} y x \end{matrix}]$
$P X = [\begin{matrix} 45 \end{matrix}]$

$∴$ $[\begin{matrix} 1 & 2 3 & 4 \end{matrix}] \times [\begin{matrix} y x \end{matrix}] = [\begin{matrix} y + 2 x 3 y + 4 x \end{matrix}]$

$\Rightarrow [\begin{matrix} y + 2 x 3 y + 4 x \end{matrix}] = [\begin{matrix} 45 \end{matrix}]$

Now,
$y + 2 x = 4$
$y = 4 - 2 x$ ...(i)
$3 y + 4 x = 5$ ... (ii)
Using (i) in (ii), we get
$3 (4 - 2 x) + 4 x = 5$
$12 - 6 x + 4 x = 5$
$2 x = 7$
$x = \frac{7}{2}$
Putting the value of $x = \frac{7}{2}$ , in (i)
$y = 4 - 2 \times \frac{7}{2}$
$y = 4 - 7$
$y = - 3$

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If P=[1234] and X=[yx], then PX=[45]. Find the value of y?-3

The correct option is A -3Given, P=[1234] X=[yx] PX=[45] ∴ [1234]×[yx]=[y+2x3y+4x] ⇒[y+2x3y+4x]=[45] Now, y+2x=4 y=4−2x...(i) 3y+4x=5... (ii) Using (i) in (ii), we get 3(4−2x)+4x=5 12−6x+4x=5 2x=7 x=72 Putting the value of x=72, in (i) y=4−2×72 y=4−7 y=−3

If $P = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $X = [\begin{matrix} y x \end{matrix}]$ , then $P X = [\begin{matrix} 45 \end{matrix}]$ . Find the value of y?
-3