VAM_23-31

# VAM_23-31 - Tutorial VAM Vector Algebra and an Introduction...

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Unformatted text preview: Tutorial VAM: Vector Algebra and an Introduction to Matrices Exercise 23. A + B = @ 2 +5 5 Â¡ 5 Â¡ 1+ 3 Â¡ 3 +1 4+ 4 2+ 3 1 Â¡ 4 7+ 2 3+ 1 1 A = @ 7 2 Â¡ 2 8 5 Â¡ 3 9 4 1 A : Exercise 24. ( Â¸ ( A + B )) ij = Â¸ ( A + B ) ij = Â¸ ( A ij + B ij ) = Â¸A ij + Â¸B ij ; where we have used Eqn. 44. Exercise 25. AB = @ 2 5 Â¡ 1 Â¡ 3 4 2 1 7 3 1 A @ 5 Â¡ 5 3 1 4 3 Â¡ 4 2 1 1 A = @ 2 Â£ 5+ 5 Â£ 1+ ( Â¡ 1) Â£ ( Â¡ 4) 2 Â£ ( Â¡ 5) +5 Â£ 4 + ( Â¡ 1) Â£ 2 2 Â£ 3+ 5 Â£ 3+ ( Â¡ 1) Â£ 1 ( Â¡ 3) Â£ 5 +4 Â£ 1 +2 Â£ ( Â¡ 4) ( Â¡ 3) Â£ ( Â¡ 5) +4 Â£ 4 +2 Â£ 2 ( Â¡ 3) Â£ 3 +4 Â£ 3+ 2 Â£ 1 1 Â£ 5 +7 Â£ 1 +3 Â£ ( Â¡ 4) 1 Â£ ( Â¡ 5) +7 Â£ 4 +3 Â£ 2 1 Â£ 3 +7 Â£ 3+ 3 Â£ 1 1 A = @ 19 8 20 Â¡ 19 35 5 29 27 1 A : Exercise 26. Â³ ~ B ~ A Â´ ik = Â³ ~ B Â´ ij Â³ ~ A Â´ jk = B ji A kj = A kj B ji = ( AB ) ki = Â³ f AB Â´ 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 Introduction...

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