VAM_23-31

VAM_23-31 - Tutorial VAM: Vector Algebra and an...

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Unformatted text preview: Tutorial VAM: Vector Algebra and an Introduction to Matrices Exercise 23. A + B = @ 2 +5 5 5 1+ 3 3 +1 4+ 4 2+ 3 1 4 7+ 2 3+ 1 1 A = @ 7 2 2 8 5 3 9 4 1 A : Exercise 24. ( ( A + B )) ij = ( A + B ) ij = ( A ij + B ij ) = A ij + B ij ; where we have used Eqn. 44. Exercise 25. AB = @ 2 5 1 3 4 2 1 7 3 1 A @ 5 5 3 1 4 3 4 2 1 1 A = @ 2 5+ 5 1+ ( 1) ( 4) 2 ( 5) +5 4 + ( 1) 2 2 3+ 5 3+ ( 1) 1 ( 3) 5 +4 1 +2 ( 4) ( 3) ( 5) +4 4 +2 2 ( 3) 3 +4 3+ 2 1 1 5 +7 1 +3 ( 4) 1 ( 5) +7 4 +3 2 1 3 +7 3+ 3 1 1 A = @ 19 8 20 19 35 5 29 27 1 A : Exercise 26. ~ B ~ A ik = ~ B ij ~ A jk = B ji A kj = A kj B ji = ( AB ) ki = f AB ik : Note that we are using the summation convention and have commuted the ordinary numbers A kj and B ji ; j of course runs over the same values throughout....
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VAM_23-31 - Tutorial VAM: Vector Algebra and an...

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