MHB Confused About Exercise 11 Answer Key

[Petrus]

Hello,

in exercise 11, I get b is not and w is, but the answer key says b is and w is not...? I don't understand...have I misunderstood or is the answer key wrong?

View attachment 1379

Regrds,
$$|\pi\rangle$$

 

[Evgeny.Makarov]

I don't know who/what facit is, but he/she/it is correct. Perhaps if you post your solution, we can discuss it.

 

[MarkFL]

Petrus, 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. :D

 

[alyafey22]

I don't know who/what facit is, but he/she/it is correct. Perhaps if you post your solution, we can discuss it.

Somehow he is referring by facit to the textbook.

 

[Petrus]

Petrus, 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. :D

What do you mean by rotate? The picture seem nice to me

 

[MarkFL]

Yes, the facit refers to the answer key (I have edited the post), and I have rotated, cropped, re-sized and uploaded the new image. (Sun)

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

 

[Petrus]

I don't know who/what facit is, but he/she/it is correct. Perhaps if you post your solution, we can discuss it.

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 $$x_3=t$$ we got $$x_2=-1-2t$$ and $$x_1= 3+t$$ it indeed got soloution so it is in col(A)
Right?

Regards,
$$|\pi\rangle$$

- - - Updated - - -

Yes, the facit refers to the answer key (I have edited the post), and I have rotated, cropped, re-sized and uploaded the new image. (Sun)

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

Strange and thanks for doing that! I did not know it needed to be rotated cause it showed correctly for me:S That is strange

 

[Evgeny.Makarov]

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

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 $$x_3=t$$ we got $$x_2=-1-2t$$ and $$x_1= 3+t$$ it indeed got soloution so it is in col(A)
Right?

Yes, but in post #1 you said that $b$ is not in $\text{col}(A)$.

 

[Petrus]

Yes, but in post #1 you said that $b$ is not in $\text{col}(A)$.

That'S cause I got actually wrong number in My matrice somehow.. Sorry My bad and now I correctly Solved it:)
Regards,
$$|\pi\rangle$$

 

[Deveno]

(3,2) = 3(1,1) + (-1)(0,1). This proves b is in col(A).

******

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.