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1. So firstly I would like to show that product of the matrices L21,L31,... in the derivation of the LU decmoposition is lower triangular. I have already shown that product of upper and lower triandular matices is upper or lower. Now I don't know how to show the derivation.

2. I have been given I - ab^T which are member or reals ^n*n. I is identity and a,b are vectors. I need to show what conditions on a and b does the inverse have the form I + ab^T ? Can anyone help me with this as well?

3. I have been given that A=uv^T and both u and v are vectors. I need to find out number of floating point operations required to compute (uv^T)x and how many operations are needed for u(v^Tx). I know that operation on uv^T is outer product of u and v but how do I show the number of floating points?

Thanks

2. I have been given I - ab^T which are member or reals ^n*n. I is identity and a,b are vectors. I need to show what conditions on a and b does the inverse have the form I + ab^T ? Can anyone help me with this as well?

3. I have been given that A=uv^T and both u and v are vectors. I need to find out number of floating point operations required to compute (uv^T)x and how many operations are needed for u(v^Tx). I know that operation on uv^T is outer product of u and v but how do I show the number of floating points?

Thanks

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