The interpretation of the given question is as follows:
Use the given inverse to solve the system of equations
[tex]x- y - z = -6 \\ \\ 2y + z = -6 \\ \\ 3x -8 y = - \dfrac{1}{2}[/tex]
The inverse of [tex]\left[\begin{array}{ccc}1&-1&1\\0&2&1\\3&-8&0\end{array}\right] is \left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right][/tex]
x =
y =
z =
Answer:
x = - 1.5
y = - 0.5
z = - 5
Step-by-step explanation:
Using the correlation of inverse of matrix AX = B to solve the question above;
AX = B
⇒ A⁻¹(AX) = A⁻¹ B
X = A⁻¹ B
So ;
X = A⁻¹ B
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =[/tex] [tex]\left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right] =[/tex] [tex]\left[\begin{array}{ccc}-6\\ -6\\- \dfrac{1}{2}\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(-8*-6)+(8*-6)+(3*-\dfrac{1}{2})\\(-3*-6)+(3*-6)+(1*-\dfrac{1}{2})\\(6*-6)+(5*-6)+(-2* - \dfrac{1}{2})\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(48)+(-48)+(\dfrac{-3}{2})\\(18)+(-18)+(\dfrac{-1}{2})\\(-36)+(30)+(1)\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(\dfrac{-3}{2})\\(\dfrac{-1}{2})\\(-5)\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-1.5\\-0.5\\ -5\end{array}\right][/tex]
