10-27 Class notes

Yesterday we found the determinant of a 2x2 matrix with entries [[a b][c d]]
as  ad - bc.

Today we used the determinant in an expression to find the inverse matrix

(1/det) [[d -b][ -c a]]

If we have a 2x2 matrix of known values times a 2x1 matrix of unknowns X  equal to a 2x1 matrix of known values,
A times [[a][ b]] = B           where X = [[a][ b]]        (see page 62, item 11)
[[ 1 1 ][0.4 0.15]] times [[a][ b]] = [[3000][ 840]]                 B = [[3000][ 840]]
we can isolate the matrix of unknowns by multiplying both sides of the equation by the inverse of the first matrix.  This simplifies the left side, isolating the 2x1 matrix of variables.

The inverse of  [[ 1 1 ][0.4 0.15]] is [[ -0.6 4][ 1.6 -4]]       (see page 63, item 12b)

[[a][ b]] = inverse of A times B

 [[a][ b]] = [[ -0.6 4][ 1.6 -4]] times [[3000][ 840]]

Homework for Friday 10-28:  page 63, item 12c; Use matrix multiplication to find a and b in the 2x1 matrix of unknowns.