hi!

i have matrix

1, 1, 0, 1

2, 1, 1, -1

3, 2, 1, 0

i am told:

(a)

i've tried performing a row echelon form on the original matrix to get

1, 1, 0, 1

2, 1, 1, -1

3, 2, 1, 0

=>

1, 1, 0, 1

0, 1, -1, 3

0, 0, 0, 0

which gives me two non-zero rows (1, 1, 0, 1) and (0, 1, -1, 3). these don't make sense for any of the x^3 - bx - cx, 2x^3 - 3x^2 + 1 or (1, 0, 1), (0, 1, 1) values given in the answer.

(b)

i've also tried switching them to columns and performing row echelon form:

1, 2, 3

1, 1, 2

0, 1, 1

1, -1, 0

=>

1, 2, 3

0, 1, 1

0, 0, 0

0, 0, 0

which again gives me two non-zero rows and i'm left with (1, 2, 3) and (0, 1, 1), which again doesn't work for what they say.

what am i doing wrong?! please any help i'm pretty worried about this! thank you!

i have matrix

1, 1, 0, 1

2, 1, 1, -1

3, 2, 1, 0

i am told:

*"a possible basis might consist of x^3 - bx - cx and 2x^3 - 3x^2 + 1. one might find the basis for the image by considering the span of the image vectors (1, 2, 3), (1, 1, 2), (0, 1, 1) and (1, -1, 0), of the standard basis of V. this should lead to the observation that the image is precisely the subspace spanned by (1, 0, 1) and (0, 1, 1)".*(a)

i've tried performing a row echelon form on the original matrix to get

1, 1, 0, 1

2, 1, 1, -1

3, 2, 1, 0

=>

1, 1, 0, 1

0, 1, -1, 3

0, 0, 0, 0

which gives me two non-zero rows (1, 1, 0, 1) and (0, 1, -1, 3). these don't make sense for any of the x^3 - bx - cx, 2x^3 - 3x^2 + 1 or (1, 0, 1), (0, 1, 1) values given in the answer.

(b)

i've also tried switching them to columns and performing row echelon form:

1, 2, 3

1, 1, 2

0, 1, 1

1, -1, 0

=>

1, 2, 3

0, 1, 1

0, 0, 0

0, 0, 0

which again gives me two non-zero rows and i'm left with (1, 2, 3) and (0, 1, 1), which again doesn't work for what they say.

what am i doing wrong?! please any help i'm pretty worried about this! thank you!

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