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## Find the matrix of a form with respect to a basis

Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.2 Solution: It is not a form! I think it should be $$f((x_1,y_1),(x_2,y_2))=x_1x_2+y_1y_2.$$Then the matrices are\[\begin{pmatrix}1 & 0\\ 0 &…

## Solve general linear equations with $2\times 2$ matrix

Solution to Linear Algebra Hoffman & Kunze Chapter 1.3 Exercise 1.3.8 Solution: (a) In this case the system of equations is \begin{alignat*}{1} 0\cdot x_1 + 0\cdot x_2 &= 0\\ 0\cdot…