16. What is the value of a that would make the matrix equation true?:
( 1 -2) (-5 6) (a b)
( 3 4) (7 -8) = (c d)
Just multiply the matrices
a = (1)(-5)+(-2)(7)
b = (1)(6)+(-2)(-8)
c = (3)(-5)+(3)(7)
d = (3)(6)+(3)(-8)
For the matrices I came up with the following:
a. -5 + -14 = -19
b. 6 + 16 = 22
c. -15 + 21 = 6
d 18 + -24 = -6
Is this right? What am I suppose to do afterwards?
To find the value of a that would make the matrix equation true, we need to solve the equation by equating the corresponding elements of the matrices.
Given equation:
( 1 -2) (-5 6) (a b)
( 3 4) (7 -8) = (c d)
We can write this equation as two separate equations by comparing the corresponding elements:
1 = -5a + 6c
-2 = -5b + 6d
Let's solve these equations simultaneously:
From the first equation:
1 = -5a + 6c
Rearranging the equation, we get:
-5a = -6c + 1
Dividing by -5, we get:
a = (6c - 1)/5
Now, substitute the value of a into the second equation:
-2 = -5b + 6d
Rearranging the equation, we get:
-5b = -6d - 2
Dividing by -5, we get:
b = (6d + 2)/5
Therefore, the value of a that would make the matrix equation true is (6c - 1)/5, and the value of b would be (6d + 2)/5.