Midterm 1

Question 1

Consistent system

Answer 1

Has at least one solution

Question 2

Inconsistent system

Answer 2

Has no solutions

Question 3

Find orthogonal vector

Answer 3

Dot vectors together, must equal zero

Question 4

Formula for finding inverse of a 2x2 matrix

Answer 4

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

Question 5

Determinant formula (2x2 matrix)

Answer 5

det(A) = ad-bc

Question 6

Finding inverse of non 2x2 matrix

Answer 6

change matrix to rref, apply same operations to an identity matrix

Question 7

system has infinitely many solutions

Answer 7

at least one free variable

Question 8

system has no solution

Answer 8

solution matrix has zero row, but corresponding vector position is non zero [A|b], [0 0 0|3]

Question 9

system has unique solution

Answer 9

for m*n matrix, rank = n (no zero rows, no free variables)

Question 10

linear dependence

Answer 10

c1v1+c2v2+c3v3=0, where at least one c is non zero

Question 11

dot product formula

Answer 11

u*v = u1v1 + u2v2 … + unvn

Question 12

length of a vector

Answer 12

||u|| = square root(u*u)

Question 13

projection of u onto v

Answer 13

proj v u = (uv / vv)*v

Question 14

angle (theta) between nonzero u and v

Answer 14

cos(theta) = (uv) / (||u||||v||)

Question 15

(AB)^-1 equivalent

Answer 15

B^-1 * A^-1