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 Exercise [13.14] 
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Post Exercise [13.14]
x^a\to \left(<br />\begin{array}{ccc}<br /> T^1{}_1 & T^1{}_2 & T^1{}_3 \\<br /> T^2{}_1 & T^2{}_2 & T^2{}_3 \\<br /> T^3{}_1 & T^3{}_2 & T^3{}_3<br />\end{array}<br />\right)\left(<br />\begin{array}{c}<br /> x^1 \\<br /> x^2 \\<br /> x^3<br />\end{array}<br />\right)

The product of two matrices T^a{}_b (3\times 3) and x^b (3\times 1) is defined as

R^a{}_c=\sum _{b=1}^3 T^a{}_bx^b

R^a{}_c=\left(T^a{}_1x^1\right)+\left(T^a{}_2x^2\right)+\left(T^a{}_3x^3\right)

Which forms a (3\times 1) matrix

x^a\to \left(<br />\begin{array}{c}<br /> \left[T^1{}_1x^1+T^1{}_2x^2+T^1{}_3x^3\right] \\<br /> \left[T^2{}_1x^1+T^2{}_2x^2+T^2{}_3x^3\right] \\<br /> \left[T^3{}_1x^1+T^3{}_2x^2+T^3{}_3x^3\right]<br />\end{array}<br />\right)

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29 May 2008, 15:19
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