Thank u so much sir. After learning your amazing approach we can even solve the tricky and tough questions very easily. Your contents has improved our thought process a lot.
I know i can pause the video and read the question by myself... But .. It want you to read the full question and little bit explain about the question. Even though it will take sometime.(hearing your voice reading the question is going to bring me a big satisfaction all together). Then start ......... Thank you so much.
Sir can you please help me to solve this question please: Let 𝑇: 𝑃1 → 𝑃2 be a linear transformation defined by 𝑇(𝑝(𝑥)) = (𝑥 + 1)𝑝(𝑥). Find the matrix for 𝑇 with respect to basis {1, 𝑥}.
You can watch the below video. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-wA2lJEtdcKE.html You will learn how to find matrix easily...Anyhow,. I give you hint.. Its a 3x2 matrix...and answer is T = [ 1 0 1 1 0 1]
Your explanation is wrong in Question on 31:08. In option d) How can you say dimension of V is 5? It's not mentioned in the question. Dimension of V can be 7 and still the minimal polynomial can be same. Number of distinct eigenvalues don't give any info about dimension of a Vector space. Example) Let's take I(Identity map)from R^3 toR^3. Dimension of Vector space R^3 is 3. Matrix of Transformation is Identity matrix of Rank 3. Its minimal polynomial is p(x) = (x-1) (That is only one particular eigen value) That doesn't mean its dimension is one.
Sir could have used the explanation as:since there are non zero distinct eigen values therefore det(A) is not equal to 0. In this case matrix becomes full rank and hence nullity is 0. Correct me sir,If I am wrong
Its the most recent question of June 2023 on 1:34:32. And you have done it completely wrong. Seems like you watching the answer key first and then trying to solve to bring the matching answers. Its answer in previous was given wrong and later it was corrcted. Correct answer is 4th. Please people don't watch his videos and ruin your concepts!
