Why are my answers for Linear Algebra homework incorrect?

In summary: I see.In summary, the student is trying to solve a multiplication problem from a textbook, but is having difficulty with some of the steps. He needs help understanding how to solve the problem correctly.
  • #1
ElliottG
24
0

Homework Statement


[URL]http://74.52.147.194/~devilthe/uploads/1317866006.png[/URL]

The Attempt at a Solution



I have gotten the matix multiplication uuT CORRECT! The only thing I can't get is the uTu part. I don't have an attempt at a solution because I have zero idea!

Second question:

Homework Statement


[URL]http://74.52.147.194/~devilthe/uploads/1317803280.png[/URL]

The Attempt at a Solution


Now, I have done this exactly per as in my notes (I hope?)

I applied the same row operations that are said in the question to the 3x3 identity matrix...yet it shows that some of them are wrong? ~85% of my answers are right but some of them aren't.

For instance, the "1/6" in E2 1st column 1st row is wrong (WTF?)

Double checks would be appreciated and even my methods!

Thanks,
Elliott
 
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  • #2
1) Yes, your [itex]uu^T[/itex] is correct.
[tex]u^Tu= \begin{bmatrix}-4 & 2 & 7 \end{bmatrix}\begin{bmatrix}-4 \\ 2 \\ 7\end{bmatrix}[/tex]
which is just like a "dot product" of the vector withitself.

2) Yes, (a) is correct. In (b) where did that "6" come from? An "elementary" matrix is, by definition, a matrix derived from the identity matrix by a single "row operation" and so can differ from the identity matrix in a single place. You are not combining (b) with (a) are you? They are completely separate questions.

Same thing in (c) and (d) you appear to be "accumulating" operations in each question and you are NOT asked to do that. Each answer should differ from the identity matrix in a single place.
 
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  • #3
HallsofIvy said:
1) Yes, your [itex]uu^T[/itex] is correct.
[tex]u^Tu= \begin{bmatrix}-4 & 2 & 7 \end{bmatrix} \begin{bmatrix}-4 \\ 2 \\ 7\end{bmatrix}[/tex]
which is just like a "dot product" of the vector withitself.

2) Yes, (a) is correct. In (b) where did that "6" come from? An "elementary" matrix is, by definition, a matrix derived from the identity matrix by a single "row operation" and so can differ from the identity matrix in a single place. You are not combining (b) with (a) are you? They are completely separate questions.

Same thing in (c) and (d) you appear to be "accumulating" operations in each question and you are NOT asked to do that. Each answer should differ from the identity matrix in a single place.

I see.

I don't understand your explanation for my question #1, though!

As for 2, I see what the problem is. I was accumulating operations because that's what we were doing in the notes for some reason...
 
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  • #4
ElliottG said:
I see.

I don't understand your explanation for my question #1, though!
uTu is the product of two matrices: a 1 x 3 matrix multiplying a 3 x 1 matrix. The product will be 1 x 1. For all intents and purposes, this is a scalar.

uTu produces the same value as u [itex]\cdot[/itex] u.
ElliottG said:
As for 2, I see what the problem is. I was accumulating operations because that's what we were doing in the notes for some reason...
 

1. What is Linear Algebra double check?

Linear Algebra double check is a process of verifying the accuracy of a calculation or solution in the field of linear algebra. It involves checking the steps and calculations used to arrive at a solution to ensure that they are correct.

2. Why is it important to double check linear algebra solutions?

Double checking linear algebra solutions is important because it helps to catch any errors or mistakes that may have been made during the calculation process. It ensures the accuracy and reliability of the results.

3. What are the common mistakes that can be caught through double checking in linear algebra?

Some common mistakes that can be caught through double checking in linear algebra include miscalculations, typographical errors, and incorrect use of formulas or equations.

4. How can I double check my linear algebra solutions?

To double check your linear algebra solutions, you can go through each step of the calculation process and compare it with your original work. You can also use online calculators or software to verify your results.

5. Can double checking linear algebra solutions guarantee 100% accuracy?

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