Linear Algebra Done Wrong20

Solution to Linear Algebra Done Wrong Exercise 1.3.7
Show that any linear transformation in $\mathbb C$ (treated as a complex vector space) is a multipli...
Solution to Linear Algebra Done Wrong Exercise 1.3.5
Let $A$ be a linear transformation. If ${\bf z}$ is the center of the straight interval $[{\bf x}, {...
Solution to Linear Algebra Done Wrong Exercise 1.3.4
Find $3\times 3$ matrices representing the transformations of $\mathbb R^3$ which:a) project every v...
Solution to Linear Algebra Done Wrong Exercise 1.3.3
For each linear transformation below find its matrix a) $T:\mathbb R^2\to \mathbb R^3$ defined by $$...
Solution to Linear Algebra Done Wrong Exercise 1.3.2
Let a linear transformation in $\mathbb R^2$ be the reflection in the line $x_1=x_2$. Find its matri...
Solution to Linear Algebra Done Wrong Exercise 1.3.1
Multiply a) $\begin{pmatrix} 1 & 2 & 3\\ 4 &5 & 6\end{pmatrix}\begin{pmatrix} 1 \\ 3...
Solution to Linear Algebra Done Wrong Exercise 1.2.6
Is it possible that vectors ${\bf v}_1$, ${\bf v}_2$, ${\bf v}_3$ are linearly dependent, but the ve...
Solution to Linear Algebra Done Wrong Exercise 1.2.5
Let a system of vectors ${\bf v}_1$, ${\bf v}_2$, $\cdots$, ${\bf v}_r$ be linearly independent but ...
Solution to Linear Algebra Done Wrong Exercise 1.2.4
Write down a basis for the space of a) $3\times 3$ symmetric matrices; b) $n\times n$ symmetric matr...
Solution to Linear Algebra Done Wrong Exercise 1.2.3
Recall, that a matrix is called symmetric if $A^T = A$. Write down a basis in the space of symmetric...