First method is to find the inverse of matrix B, and then
compare and evaluate for k. It should be a shorter method than my
2nd method, but I'm not sure if inverse matrix is in your syllabus
at the moment.
1st Method:
k (B)^ -1 =
4A + I
k (1/(2 - (-2)) * (1 1) = (
-1/4 + 1 3/4 + 0)
(-2
2) ( -6/4 + 0
2/4 + 1)
k * (1/4
1/4) =
(3/4 3/4)
(-2/4
2/4) (
-6/4 6/4)
k * (1/4
1/4) = 3 *
(1/4 1/4)
(-2/4
2/4) (
-2/4 2/4)
Comparing, k = 3
2nd Method:
k (B)^ -1 =
4A + I
k
(B)^ -1 = ( -1/4 +
1 3/4 + 0)
( -6/4 + 0 2/4 + 1)
k (B)^ -1 =
(3/4 3/4)
( -6/4 6/4)
k (B)^ -1 = 3/4 * (1
1)
( -2 2)
k (B)^ -1 * (B) = 3/4
* (1
1) * (B)
( -2 2)
k I = 3/4 * (1
1) *
(2 -1)
( -2
2)
(2 1)
k I = 3/4 * (1*2 + 1*2
1*-1 + 1*1)
(-2*2 + 2*2 -2*-1 +
2*1)
k I = 3/4 *
(4 0)
(0 4)
k I =3 I
k = 3
