Questions: Find the values of the variables in the equation. [ left[ beginarrayll -9 7 -8 0 endarray right] = left[ beginarrayrr -9 x y z endarray right] ] [ beginarrayl x=7 y=-8 z=0 endarray ]

Find the values of the variables in the equation.

[
left[
beginarrayll
-9 7
-8 0
endarray
right]
=
left[
beginarrayrr
-9 x
y z
endarray
right]
]

[
beginarrayl
x=7
y=-8
z=0
endarray
]

Transcript text: Find the values of the variables in the equation. \[ \left[\begin{array}{ll} -9 & 7 \\ -8 & 0 \end{array}\right]=\left[\begin{array}{rr} -9 & x \\ y & z \end{array}\right] \] \[ \begin{array}{l} x=\square \\ y=\square \\ z=\square \end{array} \]

Solution

Solution Steps

Step 1: Compare the corresponding elements of the matrices

The given equation is: \[ \left[\begin{array}{ll} -9 & 7 \\ -8 & 0 \end{array}\right]=\left[\begin{array}{rr} -9 & x \\ y & z \end{array}\right] \] To find the values of \( x \), \( y \), and \( z \), compare the corresponding elements of the two matrices.

Step 2: Solve for \( x \)

Compare the element in the first row and second column: \[ 7 = x \] Thus, \( x = 7 \).

Step 3: Solve for \( y \)

Compare the element in the second row and first column: \[ -8 = y \] Thus, \( y = -8 \).

Step 4: Solve for \( z \)

Compare the element in the second row and second column: \[ 0 = z \] Thus, \( z = 0 \).