Find the Matrix Representation for a Linear Transformation

[obtuse egret]

"Given a = -1, Find the Matrix Representation for a Linear Transformation with respect to standard basis of R4 and non standard basis of R3 which consists of 3 vectors: (image)"

Need help for the 2nd part of the question

[umbral reef]

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[crisp matrix]

what dimensions does this matrix have?

[obtuse egret]

uh its r3?

[crisp matrix]

how many rows/columns?

[obtuse egret]

not sure what u wanna know

its a 3x3

[crisp matrix]

what makes you think it's 3x3?

how many basis vectors are there in R4?

[obtuse egret]

4

[obtuse egret]

well its
0 1 1
1 0 1
1 1 0

[crisp matrix]

hence 4 columns

[crisp matrix]

that's a basis of R3

[obtuse egret]

yeah, i wasnt really sure when u asked what dimensions cause idk what matrix u talking about specifically

[crisp matrix]

the matrix you are looking for is 3x4

[crisp matrix]

i assume you are familiar with relevant definitions

if not, then learn them

the columns of the matrix representation of f, call it A, are the coordinates of the images of basis elements with respect to the given basis in R3

for example,

f(1,0,0,0) = (1,2,1)

now what are the coordinates of (1,2,1) with respect to the given basis?

[obtuse egret]

would it be something like:
a(0, 1, 1) + b(1, 0, 1) + c(1, 1, 0) = (1, 2, 1)
?

[crisp matrix]

correct

find a,b,c

[obtuse egret]

oh okay i think i got it now

ty! 😄

i'll close this for now

+close

[novel fjord]

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[novel fjord]

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