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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

- Thread starter Petrus
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- Jan 30, 2012

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- Jan 17, 2013

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Somehow he is referring by facit to the textbook.

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- Feb 21, 2013

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What do you mean by rotate? The picture seem nice to mePetrus, I suggest if you are going to upload images that you use some sort of image editing software to rotate the image so that it is the right side up for ease of reading.

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- Feb 21, 2013

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If we start with col(a)

after row reduce we got 1 0 -1|3

----------------------------0 1 2|-1

that means we got infinity soloution, if we set \(\displaystyle x_3=t\) we got \(\displaystyle x_2=-1-2t\) and \(\displaystyle x_1= 3+t\) it indeed got soloution so it is in col(A)

Right?

Regards,

\(\displaystyle |\pi\rangle\)

- - - Updated - - -

Strange and thanks for doing that! I did not know it needed to be rotated cause it showed correctly for me:S That is strangeYes, the facit refers to the answer key (I have edited the post), and I have rotated, cropped, re-sized and uploaded the new image.

edit: Petrus, on my computer, the image needed to be rotated clockwise 90 degrees.

- Jan 30, 2012

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in exercise 11, I get b is not and w is, but the answer key says b is and w is not...?

Yes, but in post #1 you said that $b$ isIf we start with col(a)

after row reduce we got 1 0 -1|3

----------------------------0 1 2|-1

that means we got infinity soloution, if we set \(\displaystyle x_3=t\) we got \(\displaystyle x_2=-1-2t\) and \(\displaystyle x_1= 3+t\) it indeed got soloution so it is in col(A)

Right?

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- Feb 21, 2013

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That'S cause I got actually wrong number in My matrice somehow.. Sorry My bad and now I correctly Solved itYes, but in post #1 you said that $b$ isnotin $\text{col}(A)$.

Regards,

\(\displaystyle |\pi\rangle\)

Last edited:

- Feb 15, 2012

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******

On the other question if a(1,0,-1) + b(1,1,1) = (a+b,b,b-a) = (-1,1,1), we must have

b = 1, leading to:

a+1 = -1 --> a = -2

1-a = 1 --> a = 0.

Since -2 is not 0 (unless you are in a field of characteristic two, and then there is no "3"), this is impossible.

******

Answer keys are evil...let me explain why: the point of learning math is not to get "answers" but rather, to be confident the answers you obtain are correct. Not only doesn't the "real world" come with an answer key, but one has only logical reasoning as a test of one's sanity. If one's only experience with riding a bike is with training wheels, one does not know how to ride a bike. Also, answer keys can be erroneous, and proof by authority is not a valid mathematical method.