MATH 240: EXAM 3 QUESTIONS AND CORRECT ANSWERS

MATH 240: EXAM 3 QUESTIONS AND
CORRECT ANSWERS
Column Space ✅✅ANSW-Reduce A and break it down into its vectors.



Basis ✅✅ANSW-B is a basis if...

- B is linearly independent.

- B spans V.



Coordinate Vector ✅✅ANSW-Vector from Scalars



Isomorphism ✅✅ANSW-A linear transformation that is one-to-one and onto.



Dimension ✅✅ANSW-The number of vectors in a basis of V.



Row Space ✅✅ANSW-Vectors of the rows of A.



Rank ✅✅ANSW-- rank(A) = dim(col(A))

- rank(A) + dim(null(A)) = n



Transpose ✅✅ANSW-Write the rows as columns.



Inverse ✅✅ANSW-Reduce [A I]. If A is equivalent to I, then that matrix is now [I inv(A)].
Otherwise, A isn't invertable.



Determinant ✅✅ANSW-- 2x2: ad-cb

- Triangular: multiply the items in the diagonal.

- Otherwise



Null Space ✅✅ANSW-Nul(A) = x where Ax = 0.