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What is the determinant

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Reference no: EM13914210

Question 1: Find a basis for the orthogonal complement of

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Question 2: Find a vector that is orthogonal to both

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Question 3: What is the dimension of the orthogonal complement of span

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Question 4: Let W = span

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(a) Find an orthonormal basis for W.

(b) What is the orthogonal projection of 98_5.pngonto W.

(c) Write 725_6.pngas the sum of a vector in W and a vector in W⊥.

(d) Find the projection matrix P corresponding to orthogonal projection onto W.

Question 5: If A and B are 3 × 3 matrices with det(A) = 4 and det(B) = 1. What is the determinant of C = 2AT A-1BA?

Question 6: Let A be a n × n matrix with AT = A-1. What can you say about det(A)?

Question 7: Use Cramer's rule to solve the system:

x1 + x2 + x3 = 4

x1 - x2 - x3 = 0

x1 + 2x2 + 3x3 = 9

Reference no: EM13914210

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