Solve the matrix 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 need to find the value of matrix X.
First, let's divide both sides of the equation by 2 to isolate X:
X + [[2 -8],[-4 2]] = [[2 -3],[1 -4]]
Next, we need to subtract the matrix [[2 -8],[-4 2]] from both sides to obtain X:
X + [[2 -8],[-4 2]] - [[2 -8],[-4 2]] = [[2 -3],[1 -4]] - [[2 -8],[-4 2]]
Simplifying this equation, we get:
X = [[0 0],[0 0]]
Therefore, the value of matrix X is [[0 0],[0 0]].
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]].
To solve the given matrix equation 2X + 2 [[2, -8], [-4, 2]] = [[4, -6], [2, -8]], we need to isolate the variable matrix X.
Step 1: Distribute the scalar value 2 to each element of the matrix on the left-hand side:
[[4X - 16, -6X], [-8X + 4, 4X - 16]] = [[4, -6], [2, -8]]
Step 2: Set up an augmented matrix by placing the left-hand side and right-hand side of the equation side by side:
[4X - 16, -6X | 4, -6]
[-8X + 4, 4X - 16 | 2, -8]
Step 3: Perform row operations to transform the augmented matrix to its row-echelon form or reduced row-echelon form. Let's use Gaussian elimination.
Multiply the first row by -2 and add it to the second row:
[4X - 16, -6X | 4, -6]
[0, -2X - 8 | -6, 2]
Step 4: Divide the second row by -2 to simplify the matrix:
[4X - 16, -6X | 4, -6]
[0, X + 4 | 3, -1]
Step 5: Solve for X:
From the second row, we have X + 4 = 3.
Subtract 4 from both sides: X = -1.
Therefore, the solution for the matrix equation is X = [[-1, 0], [-4, -1]].