Solve for "x" and "y" given the following matrix equation:
(2x, 0.5y, -2, 1) * (3, -2, 0, 1) = (-24, 19, -6, 5)
(the matrices are going from left to right, they're all 2x2's.)
Multiply the matrices on the left-hand side and equate cell by cell with the right to get:
the equations
6x=-24
y/2-4x=19
Solve for x and y.
The two bottom cells turn out to be -6=-6 and 5=5.
6 x +0 y = -24 so x = -4
-4 x + .5 y = 19 so y = 6
-6 + 0 = -6 true
(-2)(-2) + (1)(1) = 5 true
To solve for "x" and "y" in the given matrix equation, we need to perform matrix multiplication.
First, let's write the given equation in matrix form:
[(2x, 0.5y), (-2, 1)] * [(3, -2), (0, 1)] = [(-24, 19), (-6, 5)]
To perform the multiplication, we need to multiply corresponding elements and sum them up.
For the first element in the resulting matrix, we have:
2x * 3 + 0.5y * 0 = -24
Simplifying the equation:
6x + 0 = -24
6x = -24
x = -24 / 6
x = -4
For the second element in the resulting matrix, we have:
2x * (-2) + 0.5y * 1 = 19
Substituting the value of x:
-2 * (-4) + 0.5y = 19
8 + 0.5y = 19
0.5y = 19 - 8
0.5y = 11
y = 11 / 0.5
y = 22
Therefore, the solution is:
x = -4
y = 22