Question

find the missing values (\begin{bmatrix}-6&3\\10&5end{bmatrix}+\begin{bmatrix}a&c\\b&dend{bmatrix}=\begin{bmatrix}4&-4\\7&8end{bmatrix})
a =
b =
c =
d =

Explanation:

Step1: Solve for \(a\)

We know that for matrix addition, the corresponding elements are added. So, for the top - left element: \(-6 + a=4\).
To solve for \(a\), we add 6 to both sides of the equation: \(a = 4+6=10\).

Step2: Solve for \(b\)

For the bottom - left element: \(10 + b = 7\).
Subtract 10 from both sides: \(b=7 - 10=- 3\).

Step3: Solve for \(c\)

For the top - right element: \(3 + c=-4\).
Subtract 3 from both sides: \(c=-4 - 3=-7\).

Step4: Solve for \(d\)

For the bottom - right element: \(5 + d = 8\).
Subtract 5 from both sides: \(d=8 - 5 = 3\).

Answer:

\(a = 10\), \(b=-3\), \(c = - 7\), \(d = 3\)