Set of polynomial forming a basis for $P_2$
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I was asked to find which of these sets formed a basis for $P_2$
I got the answer wrong and cannot answer again, but its going to drive me crazy if i don't understand what I did wrong.
So...
$p_1 = 1+x, p_2 = 3x+x^2,p_3 = 1+4x+x^2$
$p_1 = 1, p_2 = 1-5x,p_3 = x, p_4 = x^2$
$p_1 = 1+3x+5x^2, p_2 = 3+x$
I expanded all of them in the form $a(p_1) + b(p_2) + c(p_3)....$
After which I put them into matrix form and calculated the determinant.
For 1. The determinant was 0 and thus not linearly independent so it does not span $P_2$
For 2. The determinant was -1 and thus linearly independent so it does span $P_2$
For 3. I got a 2 x 3 matrix for which I was not sure how to proceed as I could not calculate the determinant.
linear-algebra
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
$endgroup$
add a comment |
$begingroup$
I was asked to find which of these sets formed a basis for $P_2$
I got the answer wrong and cannot answer again, but its going to drive me crazy if i don't understand what I did wrong.
So...
$p_1 = 1+x, p_2 = 3x+x^2,p_3 = 1+4x+x^2$
$p_1 = 1, p_2 = 1-5x,p_3 = x, p_4 = x^2$
$p_1 = 1+3x+5x^2, p_2 = 3+x$
I expanded all of them in the form $a(p_1) + b(p_2) + c(p_3)....$
After which I put them into matrix form and calculated the determinant.
For 1. The determinant was 0 and thus not linearly independent so it does not span $P_2$
For 2. The determinant was -1 and thus linearly independent so it does span $P_2$
For 3. I got a 2 x 3 matrix for which I was not sure how to proceed as I could not calculate the determinant.
linear-algebra
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
$endgroup$
$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30
add a comment |
$begingroup$
I was asked to find which of these sets formed a basis for $P_2$
I got the answer wrong and cannot answer again, but its going to drive me crazy if i don't understand what I did wrong.
So...
$p_1 = 1+x, p_2 = 3x+x^2,p_3 = 1+4x+x^2$
$p_1 = 1, p_2 = 1-5x,p_3 = x, p_4 = x^2$
$p_1 = 1+3x+5x^2, p_2 = 3+x$
I expanded all of them in the form $a(p_1) + b(p_2) + c(p_3)....$
After which I put them into matrix form and calculated the determinant.
For 1. The determinant was 0 and thus not linearly independent so it does not span $P_2$
For 2. The determinant was -1 and thus linearly independent so it does span $P_2$
For 3. I got a 2 x 3 matrix for which I was not sure how to proceed as I could not calculate the determinant.
linear-algebra
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
$endgroup$
I was asked to find which of these sets formed a basis for $P_2$
I got the answer wrong and cannot answer again, but its going to drive me crazy if i don't understand what I did wrong.
So...
$p_1 = 1+x, p_2 = 3x+x^2,p_3 = 1+4x+x^2$
$p_1 = 1, p_2 = 1-5x,p_3 = x, p_4 = x^2$
$p_1 = 1+3x+5x^2, p_2 = 3+x$
I expanded all of them in the form $a(p_1) + b(p_2) + c(p_3)....$
After which I put them into matrix form and calculated the determinant.
For 1. The determinant was 0 and thus not linearly independent so it does not span $P_2$
For 2. The determinant was -1 and thus linearly independent so it does span $P_2$
For 3. I got a 2 x 3 matrix for which I was not sure how to proceed as I could not calculate the determinant.
linear-algebra
linear-algebra
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
asked Nov 28 '18 at 21:24
ForextraderForextrader
677
677
$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30
add a comment |
$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30
add a comment |
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$begingroup$
How did you compute the determinants of non-square matrices?
$endgroup$
– amd
Nov 28 '18 at 21:30
$begingroup$
HINT: How many elements must there be in a basis for $P_2$?
$endgroup$
– amd
Nov 28 '18 at 21:30