8 Linear Algebra N Let A = 3 -3 6 (a) Do the columns of A span IRS? Justify your answer. (b) Are the columns of A linearly independent?
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8 Linear Algebra
N
Let A =
3
-3
6
(a) Do the columns of A span IRS? Justify your answer.
(b) Are the columns of A linearly independent? Justify your answer.
(c) Describe all solutions to Ax = b in parametric vector form. Do the same for Ax = 0.
(d) Provide an example of each of the following:
(i) An invertible matrix
(ii) A matrix with linearly independent columns, but linearly dependent rows
(iii) A 2x2 matrix with two real eigenvalues that are different from each other
(iv) A 2x2 matrix with a single real eigenvalue and only a single eigenvector
(v) A system of 2 equations in 2 unknowns with no solutions
(e) A new streaming service charges 5 dollars per month for students, and 10 dollars per month
for everyone else. This month, the service had 55 users, and collected 425 dollars. Set up a
system of linear equations, and find the number of students using the service this month.
9 Calculus
following summation:

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