Question

K

Solve the matrix equation AX = B for X.
1 1
[42]
X =
A =
ہلے
B=
23
78

Answer 1

Explanation:

I'm impressed that they make you do this in H.S. Linear Algebra. it's good for more complex math . so that's why i'm impressed. Is this an AP class?

Ax=B is our formula. we need to know something about x, it's size

so we look at rows and columns of A, 2x2 , also we need to know about B as well it's also 2x2

so now we know, that a matrix A, of size 2x2, *x = B of size 2x2

2x2*x=2x2 .... 2x2|2x2 since the two inside number match, we can do this multiplication, and the two ouside numbers tell us the size of x... it's also a 2x2. I know, a lot of explaining to just get 2x2. Maybe that is obvious, and i'm mansplaining, :DD , but I don't know what you know.

I'll put big subscripts on my matrix variable so you can see it well. You understand the subscript is the element location in the matrix , right? 1,1 is just the top left corner element of the matrix. ect , ect.

so now we need, a1,1 * x1,1 + a1,2 * x2,1 = 2 in b1,1

then we need a2,1 * x1,1 + a2,2 * x2,1 = 7 in b2,1

next we need a1,1 * x1,2 + a1,2 * x2,2 = 3 in b1,2

finally we need a2,1 * x2,1 + a2,2 * x2,2 = 8 in b2,2

X =
`\left[\begin{array}{ccc}(3)/(2) &1\\(1)/(2) &2\end{array}\right]` I did that by observation. have you learned any RREF methods yet?