Question
solve the matrix equation 2x +2 [2 -8 -4 2] = [4 -6 2 -8]
Answers
GPT 3.5
To solve the matrix equation 2x +2 [2 -8 -4 2] = [4 -6 2 -8], we can start by simplifying the equation.
First, we multiply the scalar 2 by the matrix [2 -8 -4 2]:
2 [2 -8 -4 2] = [4 -16 -8 4].
The equation now becomes 2x + [4 -16 -8 4] = [4 -6 2 -8].
Next, we can subtract [4 -16 -8 4] from both sides of the equation to isolate 2x:
2x = [4 -6 2 -8] - [4 -16 -8 4].
Subtracting element-wise, we get:
2x = [0 10 10 -12].
Finally, we can solve for x by multiplying both sides of the equation by the inverse of the coefficient of x, which is 2:
2x * (1/2) = [0 10 10 -12] * (1/2).
This simplifies to:
x = [0 5 5 -6].
Therefore, the solution to the matrix equation is x = [0 5 5 -6].
First, we multiply the scalar 2 by the matrix [2 -8 -4 2]:
2 [2 -8 -4 2] = [4 -16 -8 4].
The equation now becomes 2x + [4 -16 -8 4] = [4 -6 2 -8].
Next, we can subtract [4 -16 -8 4] from both sides of the equation to isolate 2x:
2x = [4 -6 2 -8] - [4 -16 -8 4].
Subtracting element-wise, we get:
2x = [0 10 10 -12].
Finally, we can solve for x by multiplying both sides of the equation by the inverse of the coefficient of x, which is 2:
2x * (1/2) = [0 10 10 -12] * (1/2).
This simplifies to:
x = [0 5 5 -6].
Therefore, the solution to the matrix equation is x = [0 5 5 -6].