hw2_2 - A t is symmetric. (2)Show that A-A t is...

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MATH 223 - HOMEWORK #2 Due Friday, September 21 Problem 1. 8(a,b,f) in Section 1.3. Problem 2. 11 in in Section 1.3. Problem 3. Let P 7 be the vector space of polynomials of degree 7 or less. Define W = { p ( x ) P 7 | p (1) = p (2) = ... = p (5) = 0 } . (1)Show that W is a subspace of P 7 . (2)What is the intersection W P 4 ? (Recall how many zeroes can a polynomial of degree 4 have.) Problem 4. 5(b,e,g) in in Section 1.4. Problem 5. 6 in Section 1.4. Problem 6. 10 in Section 1.4. Problem 7. Let A be a n × n matrix. (1)Show that A +
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Unformatted text preview: A t is symmetric. (2)Show that A-A t is skew-symmetric. (3)Notice that A can be written as a sum of a symmetric and a skew-symmetric matrix A = 1 2 ( A + A t ) + 1 2 ( A-A t ). Show that such an expression is unique: if A = B + C, where B is symmetric and C is skew-symmetric, then B and C are the matrices 1 2 ( A + A t ) and 1 2 ( A-A t ).(Hint: if not, we get that a symmetric matrix equals a skew-symmteric matrix.) 1...
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