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Nilai
x,y,z dan
w yang memenuhi

[[3x,0","5y],[2z,omega]]=[[x,y+1],[5,z+1]]+[[5,2+y],[0","25 z,4]]

Nilai $x, y, z$ dan $w$ yang memenuhi $\newline$ $\left[\begin{array}{cc} 3 x & 0,5 y \\ 2 z & \omega \end{array}\right]=\left[\begin{array}{ll} x & y+1 \\ 5 & z+1 \end{array}\right]+\left[\begin{array}{ll} 5 & 2+y \\ 0,25 z & 4 \end{array}\right]$

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Add three or more integers

Full solution

Q. Nilai

x, y, z

dan

w

yang memenuhi

\newline

\left[\begin{array}{cc} 3 x & 0,5 y \\ 2 z & \omega \end{array}\right]=\left[\begin{array}{ll} x & y+1 \\ 5 & z+1 \end{array}\right]+\left[\begin{array}{ll} 5 & 2+y \\ 0,25 z & 4 \end{array}\right]

Write Matrix Equation: Write down the given matrix equation. $\newline$ $\begin{bmatrix} 3x & 0 & 5y \ 2z & w \end{bmatrix} = \begin{bmatrix} x & y+1 \ 5 & z+1 \end{bmatrix} + \begin{bmatrix} 5 & 2+y \ 0 & 25z & 4 \end{bmatrix}$
Add Matrices: Add the matrices on the right-hand side of the equation. $\newline$ To add matrices, we add the corresponding elements. $\newline$ \left[\begin{array}{cc}\(\newlinex & y+1 (\newline\)5 & z+1 $\newline$ \end{array}\right]\) + \left[\begin{array}{cc}\(\newline5 & 2+y (\newline\)0 & 25z $\newline$ \end{array}\right]\) = \left[\begin{array}{cc}\(\newlinex+5 & (y+1)+(2+y) (\newline\)5 & (z+1)+(25z)+4 $\newline$ \end{array}\right]\) $\newline$ Simplify the elements: $\newline$ \left[\begin{array}{cc}\(\newlinex+5 & y+1+2+y (\newline\)5 & z+1+25z+4 $\newline$ \end{array}\right]\) = \left[\begin{array}{cc}\(\newlinex+5 & 2y+3 (\newline\)5 & 26z+5 $\newline$ \end{array}\right]\)
Set Equations Equal: Set the corresponding elements of the matrices equal to each other. $\newline$ From the first row, first column: $3x = x+5$ $\newline$ From the first row, second column: $0 = 2y+3$ $\newline$ From the first row, third column: $5y = y+1+2+y$ $\newline$ From the second row, first column: $2z = 5$ $\newline$ From the second row, second column: $w = 26z+5$
Solve for Variables: Solve the equations obtained in Step $3$ for $x$ , $y$ , $z$ , and $w$ . For $3x = x+5$ , subtract $x$ from both sides: $2x = 5$ , so $x = \frac{5}{2}$ or $x = 2.5$ For $0 = 2y+3$ , subtract $3$ from both sides: $y$ $0$ , so $y$ $1$ or $y$ $2$ For $y$ $3$ , simplify the right side: $y$ $4$ , subtract $y$ $5$ from both sides: $y$ $6$ , so $y$ $7$ or $y$ $8$

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