Consider the basis 𝐵 of ℝ^2 consisting of vectors..

Question

Consider the basis B of R^2 consisting of vectors

| 1 | | 5 |

| 5 | and | 2 |

Find 𝑥⃗ in ℝ^2 whose coordinate vector relative to the basis 𝐵 is [𝑥⃗ ]_B=

| -4 |

| 2 |

𝑥⃗ = | _ |

| _ |

Answer 1

-4<1, 5> + 2<5, 2> = <-4, -20> + <10, 4> = <6, -16>