Explanation:
Consider the following matrix equation:
Applying the additive property, this is equation is equivalent to:
[tex]\begin{bmatrix}{a-2} & {b+5} & {} & {} \\ {c\text{ -10}} & {d\text{ +6}} & {} & {} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\text{ }\begin{bmatrix}{4} & {8} & {} & {} \\ \text{ -}{1} & {0} & {} & {} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]
This is equivalent to the following linear system of equations:
Equation 1:
[tex]a\text{ - 2 = 4}[/tex]
Equation 2:
[tex]b+5=8[/tex]
Equation 3:
[tex]c\text{ -10= -1}[/tex]
Equation 4:
[tex]d\text{ +6=0}[/tex]
From equation 1, we get:
[tex]a\text{ = 4+2=6}[/tex]
From equation 2, we get:
[tex]b=8\text{ - 5 = 3}[/tex]
From equation 3, we get:
[tex]c\text{ = -1+10 = 9}[/tex]
From equation 4, we get:
[tex]d\text{ = -6}[/tex]
we can conclude that the correct answer is:
Answer:[tex]a\text{ = 6}[/tex]
[tex]b=\text{ 3}[/tex]
[tex]c\text{ = 9}[/tex]
and
[tex]d\text{ = -6}[/tex]
