Fatoom Alsaadi

Fatoom Alsaadi

Answered question

2022-03-31

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-04-26Added 556 answers

To solve this problem, we need to find the coordinates of the vector w with respect to the given basis S, and then use those coordinates to find the vector w.
Let's call the coordinates of w with respect to S x, y, and z, respectively. Then we can write:
[w]S=x[314]+y[256]+z[148]
We also know that the coordinate vector of w with respect to S is [6,-3,2], so we can set up the following system of equations:
{3x+2y+z=6x+5y+4z=34x+6y+8z=2
Solving this system of equations, we get:
x=2,y=1,z=0
Therefore, the coordinates of w with respect to the basis S are (2,-1,0). To find w itself, we can use these coordinates to write:
[w]S=2[314][256]=[436]
So we have:
w=4[314]3[256]+0[148]=[6110]
Therefore, the vector w is [6110].

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