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solution3

# solution3 - M341 Homework Solution 3 Section 1.4 1(d 8 4 6...

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Section 1.4 - 1(d) 2 A = 8 4 6 0 10 2 12 2 4 . 4 B = 24 4 0 8 8 16 12 4 4 2 A 4 B = 32 8 6 8 2 14 0 6 8 . Section 1.4 - 1(k) 4 D = [ 28 4 16 12 8 32 . ] 2 F T = [ 16 4 10 2 0 6 ] 4 D + 2 F T = [ 12 8 6 10 8 26 ] Section 1.4 - 3(b) A = 1 0 4 3 3 1 4 1 0 A T = 1 3 4 0 3 1 4 1 0 The following matrix is symmetric: 1 2 ( A + A T ) = 1 3 / 2 0 3 / 2 3 1 0 1 0 The following matrix is skew symmetric: 1 2 ( A A T ) = 0 3 / 2 4 3 / 2 0 0 4 0 0 And A = 1 2 ( A + A T ) + 1 2 ( A A T ) Section 1.4 - 6(a) : The ( i, j ) th entry of A + B is a ij + b ij . If i ̸ = j the a ij = 0 and b ij = 0 since A and B are diagonal. Therefore, for i ̸ = j , the ( i, j ) th entry of A + B is 0 and A + B is diagonal. 1

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solution3 - M341 Homework Solution 3 Section 1.4 1(d 8 4 6...

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