2.1 - 2.1 Matrix Operations Given m × n matrix A =...

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Unformatted text preview: 2.1 Matrix Operations Given m × n matrix A = bracketleftBig vector a 1 | vector a 2 | · · · | vector a n bracketrightBig , call a ij the i th entry in the j th column diagonal entries are a 11 ,a 22 , · ·· diagonal matrix = square matrix with only nonzero di- agonal entries zero matrix O- m × n matrix with all elements zero EX: 2 × 4 matrix A = bracketleftBigg 1 8 0 9 − 2 − 3 4 1 bracketrightBigg a 23 = 4 diagonal entries 1 , − 3 2 × 4 zero matrix O = bracketleftBigg 0 0 0 0 0 0 0 0 bracketrightBigg a 41 =? What about adding matrices? No problem, as long as they are both the same size – same number of rows and columns EX: 2 1 4 − 8 3 + − 2 4 − 1 − 1 4 = 1 8 − 9 2 4 1 − 2 4 − 1 − 1 4 + 2 1 4 − 8 3 = ? Properties of Matrix Addition: m × n A,B,C , scalars s,t · A + B = B + A · s ( A + B ) = sA + sB · ( A + B ) +...
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2.1 - 2.1 Matrix Operations Given m × n matrix A =...

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