what is the solution of the matrix equation?
[9 4, 2 1] X = [-9 -6, -1 -8]
A)[5 -26 9 -60]
B)[-5 26 -1 -8]
C)[-5 26 9 -60]
D)[9 26 9 1]
The correct solution to the matrix equation is:
A) [5 -26, 9 -60]
To find the solution of the matrix equation [9 4; 2 1] X = [-9 -6; -1 -8], we can follow these steps:
Step 1: Write the given matrix equation as a system of linear equations.
9x + 4y = -9
2x + y = -6
x = -1
y = -8
Step 2: Write the solution as an ordered pair (x, y).
The solution is (-1, -8).
Therefore, the correct option is Option D) [-1 -8].
To solve the matrix equation [9 4, 2 1] X = [-9 -6, -1 -8], we need to find the matrix X that satisfies the equation.
Let's call the matrix X as [a b, c d], where a, b, c, and d are unknowns.
Now equating the corresponding elements, we can set up the following equations:
For the first row:
9a + 4c = -9 (Equation 1)
9b + 4d = -6 (Equation 2)
For the second row:
2a + c = -1 (Equation 3)
2b + d = -8 (Equation 4)
We can solve this system of linear equations to find the values of a, b, c, and d.
By solving the equations, we find that a = -5, b = 26, c = 9, and d = -60.
Therefore, the solution to the matrix equation is X = [-5 26, 9 -60].
The answer is option C) [-5 26 9 -60].