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(Solved): Determine the matrix of the following bilinear forms relative to the standard basis of app ...
Determine the matrix of the following bilinear forms relative to the standard basis of appropriate vector space: (a) \( 2 x_{1} y_{1}-3 x_{1} y_{3}+2 x_{2} y_{2}-5 x_{2} y_{3}+4 x_{1} y_{2} \) (b) \( 2 x_{1} y_{1}+x_{1} y_{2}+x_{1} y_{3}+3 x_{2} y_{1}-2 x_{2} y_{3}+x_{3} y_{2}-5 x_{3} y_{3} \)
Expert Answer
If f is a bilinear form on V and B={b1,...,bn} is a basis for V then we define the matrix of f with respect to B by [f]B=[f(b1,b1)…f(b1,bn)???f(bn,b1