Linear Algebra Final exam review: Part 1

Welcome to to calculus II final exam review! In this video, we go over a standard final exam review for Linear algebra. Feel free to use the timestamps to go the question you wish! Please not that because the exam review is so large, it has been split into two parts.

00:00 - Introduction
01:02 - Question 1 (Elementary row operations)
11:47 - Question 2 (The inverse of a matrix)
17:48 - Question 3 (Proof based question for multiplication)
22:27 - Question 4 (Inverse of a matrix with properties)
26:36 - Question 5 (Inverse of a matrix with matrices and properties)
37:14 - Question 6 (Matrix transposes)
43:10 - Question 7 (Finding values of C so that a system has 1 solution, no solution or infinitely many solutions)
51:38 - Question 8 (Finding multiple values so that a system has 1 solution, no solution or infinitely many solutions)
58:26 - Question 9 (Properties of a matrix with size)
1:03:03 - Question 10 (Transformation matrix and invertibility)
1:14:53 - Question 11 (Transformation matrix + Nullity of a matrix)
1:25:15 - Question 12 (Finding a transformation matrix with standard coordinates + Invertibility)
1:35:51 - Question 13 (The adjoint of a matrix)
1:36:53 - Question 14 (Determinants with orthogonal matrices)
1:39:35 - Question 15 (Determinants with matrix properties and RREF)
1:43:48 - Question 16 (Determinants with triangular matrices)
1:50:00 - Question 17 (Determinants and parallelipipeds)
1:58:07 - Question 18 (Unknown values for parallelipipeds)
2:01:02 - Question 19 (Area of a triangle)
2:04:46 - Question 20 (Planes and subspaces)

The remaining 20 questions are in part 2!

[indunallareddy]

You have no idea how much we all appreciate you! You're an actual Godsend. Thank you :))

[adamkp_]

God bless you. I hope you find all the happiness in the world.

[Patchoulis]

I've noticed you could have sped up the process for solving question 17 by doing the dot product of the normal vector with the normal vector scaled by some value 'k', and made the absolute value of the result equal to the area 9, as ya found in the previous part, you could do the entire question using only one equation instead of 3 by solving for 'k' and multiplying it by +- the normal vector. In all, it's an amazing review for 102, so keep up the amazing work!

[abdallababikir]

27:35 why was I still able to find an inverse using the regular [A:I] formula? I understand that det(A)=0 means it's not invertible.

[KabeebLamihd]

The sad thing is at my Uni calculators are not allwoed, pluse there are no short answers, all marks are based on show your work though. only about 12 long answers questions.

[fabihazihan]

Hi! Just a bit confused for question 11, statement 4, could you please explain how the nullity can be any number greater than 1 because since it's a 2 by 3 matrix, so rank + nullity = 3. Does the nullity not need to be less than 3?
Thanks so much for the review!

[dimitrivahlas]

For question 6, I notice you go back and forth between which side you put your inverses when cancelling. Does it matter or can i just put it on any side?

[bobriss]

Just curious about your counter example for Q3 step 3. Since the claim says A^2 and not A*B, would your counter example not have to be A*A? Why would A*B work as a counter example, since that isn't A*A

[wqpvwze]

For question 7, I am a bit confused about how we determine that there are infinitely many solutions if C = 0 or 1 since we have a pivot in every column and then either [-1, 1, 0] transpose or [0, 1, 0] transposes our augmented matrix. I was hoping that you would be able to explain this.

[teamx]

Hey! Question 17, where did you get the vector (-3, -1, 2) while dotting with h?

Thanks a ton for the review!

[jeffsinclair]

Hi! for question 20 I got the same answers as you, but when I checked the answer keys it said that W was indeed a subspace and the 0 vector somehow satisfied the equation which I was confused on. Do you know why this might be?

[tjkkobo]

do you have any videos on linear transformations?

[giuseppegreco]

the last problem the equation of the plane is x-2y+3z = 6, i think you made a mistake in calculating the normal, writing -12 instead of 12. Anyway great video, very helpful