Questions: Find the values of the variables in the equation. [ left[beginarrayrr s-5 t+2 -8 -3 endarrayright]=left[beginarrayrr 8 2 -8 r endarrayright] ] [ beginarrayl r=-3 s=13 t=0 endarray ]

Find the values of the variables in the equation.

[
left[beginarrayrr
s-5 t+2
-8 -3
endarrayright]=left[beginarrayrr
8 2
-8 r
endarrayright]
]

[
beginarrayl
r=-3
s=13
t=0
endarray
]

Transcript text: Find the values of the variables in the equation. \[ \left[\begin{array}{rr} s-5 & t+2 \\ -8 & -3 \end{array}\right]=\left[\begin{array}{rr} 8 & 2 \\ -8 & r \end{array}\right] \] \[ \begin{array}{l} \mathrm{r}=-3 \\ \mathrm{~s}=13 \\ \mathrm{t}=4 \end{array} \]

Solution

Solution Steps

Step 1: Solve for \(s\)

To find \(s\), we use the equation \(s - a = e\). Substituting the given values, we get \(s - 5 = 8\), which simplifies to \(s = 8 + 5\). Therefore, \(s = 13\).

Step 2: Solve for \(t\)

To find \(t\), we use the equation \(t + b = f\). Substituting the given values, we get \(t - 2 = 2\), which simplifies to \(t = 2 + 2\). Therefore, \(t = 4\).

Step 3: Solve for \(r\)

Since \(r\) is directly given as the element in the second row and second column of the matrix, \(r = d\). Therefore, \(r = -3\).