Solve for X using the matrices below.
2A + 4B = −2X
A=
((8,-5)
(9,0)
(5,-6))
B=
((0,7)
(4,0)
(-6,-1))
oobleck got it!
2A + 4B =
(16,-10) + (0,28) = (16,18)
(18,0) + (16,0) = (34,0)
(10,-12) + (-24,-4) = (-14,-16)
so, X = -1/2 times all that:
((-8,-9)
(-17,0)
(7,8))
To solve for X, we need to rearrange the equation and isolate the variable.
Given equation: 2A + 4B = -2X
First, we need to calculate the values of 2A and 4B:
2A =
2 * A =
2 * ((8,-5), (9,0), (5,-6))
= ((16,-10), (18,0), (10,-12))
4B =
4 * B =
4 * ((0,7), (4,0), (-6,-1))
= ((0,28), (16,0), (-24,-4))
Now, let's rewrite the equation with the calculated values:
((16,-10), (18,0), (10,-12)) + ((0,28), (16,0), (-24,-4)) = -2X
Combine the corresponding elements of the matrices:
((16+0,-10+28), (18+16,0+0), (10-24,-12-4)) = -2X
((16,18), (34,0), (-14,-16)) = -2X
Next, we need to multiply both sides of the equation by -1/2 to isolate X (the variable):
-1/2 * ((16,18), (34,0), (-14,-16)) = -1/2 * -2X
Simplify:
(-8,-9), (-17,0), (7,8) = X
Therefore, the solution for X is:
X =
((-8,-9)
(-17,0)
(7,8))
To solve for X using the matrices A and B, we need to rearrange the equation 2A + 4B = -2X.
First, let's multiply each matrix by its respective scalar factor:
2A = 2 * ((8,-5), (9,0), (5,-6)) = ((16,-10), (18,0), (10,-12))
4B = 4 * ((0,7), (4,0), (-6,-1)) = ((0,28), (16,0), (-24,-4))
Next, we add the resulting matrices together:
2A + 4B = ((16,-10), (18,0), (10,-12)) + ((0,28), (16,0), (-24,-4))
= ((16+0, -10+28), (18+16, 0+0), (10-24, -12-4))
= ((16, 18), (34, 0), (-14, -16))
Now, we have the equation ((16,18), (34,0), (-14,-16)) = -2X.
To solve for X, we need to isolate X. Divide both sides of the equation by -2:
(-2X) / -2 = ((16,18), (34,0), (-14,-16)) / -2
X = ((-16/-2,-18/-2), (-34/-2,0/-2), (14/-2,16/-2))
X = ((8,9), (-17,0), (-7,8))
Therefore, the solution for X is ((8,9), (-17,0), (-7,8)).