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?
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!
Yes you're not wrong but since I used the same logic in statement 3, I figured the same logic was implied and I didn't feel like writing it because it was redundant.
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!
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.
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?
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.
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
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
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Thank you so much! Good luck on your final exams :) .
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?
Doesn't matter.
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!
Yes you're not wrong but since I used the same logic in statement 3, I figured the same logic was implied and I didn't feel like writing it because it was redundant.
Hey! Question 17, where did you get the vector (-3,-1,2) while dotting with h?
Thanks a ton for the review!
V cross w.
Took the determinant using cross product
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!
Yes that's okay too. That wasn't my first thought when I was solving.
can u explain what u mean please
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.
You could but it won't work because you won't get identity on the left side.
@@MathforThought Ohhh that makes sense! thank you
do you have any videos on linear transformations?
It's in the final exam review. I haven't made individual videos due to time though.
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.
That's unfortunate :( .
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?
Not sure what you are looking at but that's wrong.
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.
Because one of the columns is a non pivot column so there are free variables.
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
My example is fine. My point was to show IN GENERAL, this is not true.
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
Thank you for pointing that out!