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grandymaker [24]
3 years ago
15

What are the coordinates of (3 comma space 8 )relative to the basis open curly brackets space (1 comma space 1 )comma space (0 c

omma space 1 )space close curly brackets
Computers and Technology
1 answer:
Snowcat [4.5K]3 years ago
5 0

Answer:

(3,5)

Explanation:

Given the basis β={(1,1),(0,1)} and x=(3,8), I am to find the corresponding coordinate vector [x]β. I claim that the coordinate vectors entries x_{1} and x_{2} meet the following criterion:

x_{1} (1,1) +x_{2} (0,1)=(3,8)

Placing this in matrix form

\left(\begin{array}{cc}1 & 0\\ 1 & 1 \end{array} \right)\left(\begin{array}{c}x_{1} \\ x_{2}\end{array} \right)

x_{1} +0x_{2} =3

x_{1} =3

Also,

1x_{1} +1x_{2} =8

3 + 1x_{2} =8

x_{2} =8-3=5

The coordinate matrix therefore is given as (3,5)

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