The question and matrices of problem 11 are attached I need help with this please 2(a) A 0100and b =3(b) A 1 1 and b =440 16Compute the projection matrices P₁ and P₂ onto the column spaces in Problem 11.Verify that P₁b gives the first projection p₁. Also verify P2 = P2.

(a) Here given that here we have to find out the projection matrix onto the column space of A Let,…

Answered: (a) A 0 1 and b= 23 (b) A= and b= 4 00…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the following matrices, solve the questions below and if you can’t solve the problem, explain why:
For this problem enter matrices using bracket notation. So the matrix 2 3 -1] +] -2 -5 6 would be entered as [[2,3,-1],[-2,-5,6]]. Find an LU factorization for 14 -7 -14] -12 18 24 18 -30-30 8 16 L U= = 8
Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute. Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other words, provide two matrices A and B such that AB= BA. But, this time, make sure your matrices A and B are not diagonal. In the table below, enter your matrices A and B and verify that their products AB and BA are the same. Simplify your results as much as possible. A B АВ B BA Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3 diagonal matrices. Conclusion. From the results of this and previous exercises, we have found that the set D commutative under matrix multiplication because AB = BA for matrices A and B in D By contrast, note that M commutative because AB = BA for matrices A and B in M. So, while M is not there exist subsets of M which are. And, D is just one example: can you think of others?
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For this problem enter matrices using bracket notation. So the matrix 2 3 -1] -2 -5 6 would be entered as [[2,3,-1],[-2,-5,6]]. Find an LU factorization for -2 0 -67 4 14 L = U= -9 7 -27 35
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Use the dot method to add the numbers below. If the number needs a dot, put a dot (period) to the right of the number. Otherwise leave it blank.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will no Tutorial Exercise Find x and y. X + 2 3. -8 2x + 5 3 -8 4 2y 2x 4 16 -6 8-9 y+ 2 8-9 10 Step 1 Recall that if two matrices are equal then their corresponding entries are equal. Using this fact, write an equation using entries corresponding to a1 and solve it. Remember is the entry in the /th row and th column. X + 2 = Subm Skip (you cannot come back) Need Help? Read it

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(a) A 0 1 and b= 23 (b) A= and b= 4 00 4 6 Compute the projection matrices P₁ and P2 onto the column spaces in Problem 11. Verify that P₁b gives the first projection p₁. Also verify P² = P₂.