Solve the matrix equation. x-[2 -8];[-4 2] = [4 -6];[2 -8]
To solve the matrix equation, we need to find the value of x that satisfies the equation x - A = B, where A and B are matrices.
Given:
x - [2 -8]
[-4 2] = [4 -6]
[2 -8]
To solve this equation, we can add the matrix A to both sides:
x = B + A
x = [4 -6]
[2 -8] + [2 -8]
[-4 2]
Performing the matrix addition, we get:
x = [4+2 -6+(-8)]
[2+(-4) -8+2]
Simplifying further, we have:
x = [6 -14]
[-2 -6]
Therefore, the solution to the matrix equation is:
x = [6 -14]
[-2 -6]
To solve the matrix equation:
x - [2 -8] = [4 -6]
[2 -8]
We need to isolate x on one side of the equation.
Step 1: Subtract the matrix [2 -8; 2 -8] from both sides of the equation:
x - [2 -8; -4 2] - [2 -8; 2 -8] = [4 -6; 2 -8] - [2 -8; 2 -8]
Simplifying, we get:
x - [0 0; -6 10] = [2 2; 0 -2]
Step 2: Add the inverse of the matrix [0 0; -6 10] to both sides of the equation:
x - [0 0; -6 10] + [0 0; -6 10] = [2 2; 0 -2] + [0 0; -6 10]
Simplifying, we get:
x = [2 2; -6 8] + [0 0; -6 10]
Step 3: Add the corresponding elements of the matrices:
x = [2+0 2+0; -6-6 8+10]
[2 2; -12 18]
Simplifying further, we get:
x = [2 2; -12 18]
Therefore, the solution to the matrix equation is:
x = [2 2]
[-12 18]
To solve the matrix equation, we need to perform matrix subtraction on both sides of the equation.
Given the equation:
x - [2 -8; -4 2] = [4 -6; 2 -8]
To subtract the matrices, we subtract the corresponding elements in each matrix.
x - [2 -8; -4 2] = [4 -6; 2 -8]
=> [x - 2 -(-8) x -(-8);
x - (-4) - 2 x - 2] = [4 -6; 2 -8]
=> [x - 2 + 8 x + 8;
x + 4 - 2 x - 2] = [4 -6; 2 -8]
=> [9x + 6;
- x + 2] = [4 -6; 2 -8]
Now, we can equate each element in the resulting matrix equation to solve for x.
9x + 6 = 4 => 9x = 4 - 6 => 9x = -2 => x = -2/9
-x + 2 = -6 => -x = -6 - 2 => -x = -8 => x = 8
Therefore, the solution to the matrix equation is x = -2/9.