Question

Solve the matrix 2X+2 [[2 -8],[-4 2]] = [[4 -6],[2 -8]]

Answer 1

To solve the matrix equation 2X + 2 [[2 -8], [-4 2]] = [[4 -6], [2 -8]], we need to isolate X.

Let's first distribute the scalar 2 through the matrix on the left-hand side:

2X + [[4 -16], [-8 4]] = [[4 -6], [2 -8]]

Subtracting [[4 -6], [2 -8]] from both sides, we have:

2X + [[4 -16], [-8 4]] - [[4 -6], [2 -8]] = [[4 -6], [2 -8]] - [[4 -6], [2 -8]]

This simplifies to:

2X + [[0 -10], [-10 12]] = [[0 0], [0 0]]

Next, subtract [[0 -10], [-10 12]] from both sides:

2X + [[0 -10], [-10 12]] - [[0 -10], [-10 12]] = [[0 0], [0 0]] - [[0 -10], [-10 12]]

This results in:

2X = [[0 0], [0 0]]

Finally, divide both sides by 2:

2X/2 = [[0 0], [0 0]]/2

This simplifies to:

X = [[0 0], [0 0]]

Therefore, the solution to the matrix equation is X = [[0 0], [0 0]].