Finding the coordinate vector relative to a given basis

linear-algebra

Solution 1:

Since $$ 5\cdot \pmatrix{1\\-1\\3}+(-1)\cdot\pmatrix{-3\\4\\9} = \pmatrix{5\\-5\\15}+\pmatrix{3\\-4\\-9} = \pmatrix{8\\-9\\6}, $$ your solution is correct.

Maybe you copied the wrong numbers from your textbook?

Related

Cholesky of matrix plus identity
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
Is it possible to find indefinite integral of $\int \frac{1} {{\sin(x)+\sec^2(x)}}\mathrm{d}x$?
Why is second smallest eigenvalue and the corresponding eigenvector used to partition a graph?
Decomposition of an algebraic number into a sum or product of algebraic numbers with smaller degree
Prove conjecture $a_{n+1}>a_{n}$ if $a_{n+1}=a+\frac{n}{a_{n}}$
Another beauty hidden in a simple triangle (2)
"Continuized" Taylor Series? $\sin(x)=\sum \frac{(-1)^nx^{2n+1}}{(2n+1)!}=\int_{-1}^\infty \frac{\cos(\pi n) x^{2n+1}}{G(2n+1)}dn$?
Tricky Integral -- $\int_0^1 \sqrt{x^2-4x+3} \arcsin(x)~dx$
What are the isomorphism classes of $\pi_1(\mathbb{R}^2\setminus C)$ where $C$ ranges over all countable subsets of $\mathbb{R}^2$?
$\operatorname{rank} A = \operatorname{rank} A^2$ if and only if $\lim_{\lambda \to 0} (A+\lambda I)^{-1}A$ exists
How large is the area that the bug can access?