3.3/4.1/4.2

Question 1

how do you use cramers rule?

Answer 1

if you’re solving a system of linear equations (Ax=b)for x_n. replace column n with b then take the det then put the det over det A.

Question 2

formula for A^-1

Answer 2

1/det A (adj A)

Question 3

what’s adj A?

Answer 3

matrix of Cofactors of A. The row 1 col 1 entry is the Cofactor of A_11

Question 4

how you find the area of parallelogram?

Answer 4

move it so the bottom left vertex is at the origin then take the det of the top left (a,b) and bottom right (c,d). Then absolute value it

Question 5

how do you take the volume of a parallelepiped?

Answer 5

move on vertex to the origin. then make the vertices into a 3x3 matrix. [a d g; b e h; c f i]. Then take the absolute value of det

Question 6

how do you find the area of the linear transformation of a parallelogram T(S)?

Answer 6

area of T(S) = |det of two vectors given that you make a 2x2 matrix| * area of original parallelogram