solve the matrix equation 2x +2 [2 -8 -4 2] = [4 -6 2 -8]
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].
To solve the matrix equation, follow these steps:
Step 1: Write the matrix equation in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
Given equation: 2x + 2 [2 -8 -4 2] = [4 -6 2 -8]
Rewriting the equation: [2x] + [4 -16 -8 4] = [4 -6 2 -8]
Step 2: Subtract the matrix [4 -16 -8 4] from both sides of the equation.
[2x] = [4 -6 2 -8] - [4 -16 -8 4]
Simplifying, [2x] = [0 10 10 -12]
Step 3: Divide both sides of the equation by 2 to isolate the variable matrix, X.
[2x] / 2 = [0 10 10 -12] / 2
Simplifying, [x] = [0/2 10/2 10/2 -12/2]
Therefore, the solution to the matrix equation is x = [0 5 5 -6].
To solve the matrix equation 2x + 2 [2 -8 -4 2] = [4 -6 2 -8], we will follow these steps:
Step 1: Distribute the scalar 2 into the matrix [2 -8 -4 2] by multiplying each element by 2.
2 [2 -8 -4 2] = [4 -16 -8 4]
Now, the matrix equation becomes:
2x + [4 -16 -8 4] = [4 -6 2 -8]
Step 2: Subtract the matrix [4 -16 -8 4] from both sides:
2x = [4 -6 2 -8] - [4 -16 -8 4]
Performing the subtraction yields:
2x = [0 10 10 -12]
Step 3: Divide both sides of the equation by 2:
(1/2) * 2x = (1/2) * [0 10 10 -12]
Simplifying:
x = [0 5 5 -6]
So, the solution to the matrix equation is x = [0 5 5 -6].