- #1

peroAlex

- 35

- 4

Hello, everybody!

I would really appreciate if someone could help me understand how to solve the following two tasks. I am not sure whether my translation is correct, so if, by any chance, you know a more appropriate terminology, please let me know. I am not fluent in writing matrices here on the forum, therefore I've attached my attempt at a solution as a picture.

If you believe I should disclose something here, please let me know. Those are basic linear algebra tasks, so I believe there should be no problem (and yet I fail to understand it).

Please, check the attached picture.

I would really appreciate if someone could help me understand how to solve the following two tasks. I am not sure whether my translation is correct, so if, by any chance, you know a more appropriate terminology, please let me know. I am not fluent in writing matrices here on the forum, therefore I've attached my attempt at a solution as a picture.

**1. The problem statement, all variables, and given/known data**

Task 1:Prove that vectors ## v_1 = (1,1,1) ##, ## v_2 = (1,1,2) ## and ## v_3 = (1,2,3) ## form basis of vector space ## \mathbb{R}^3 ## and develop vector ## y = (6,9,14) ## according to such basis.Task 1:

**Task 2:**Linear transformations maps vectors forming standard basis into vectors (1,4,-1), (2,-3,1) and (4,3,-2). How would such transformation affect vector ## v = (1,-1,2) ##? Also, which vector is mapped into ## w = (6,11,-4) ##?## Homework Equations

If you believe I should disclose something here, please let me know. Those are basic linear algebra tasks, so I believe there should be no problem (and yet I fail to understand it).

## The Attempt at a Solution

Please, check the attached picture.