GATE IT 2006 | Question: 76

Question

• $x  + y/2 =  9$
• $3x  + y = 10$

The value of the Frobenius norm for the above system of equations is

• A. $0.5$
• B. $0.75$
• C. $1.5$
• D. $2.0$

Comments

@ Arjun Sir

Is this in Gate Syllabus ?

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Out of syllabus

Answer 1

Answer: D

Frobenius norm = $\sqrt{trace(A*A)}$ = 2.23 which is close to option D.

Comments

if we take formula given by you, and count matrix as below:

$\begin{bmatrix} 1 & 1/2 & 9\\ 3& 1& 10 \end{bmatrix}$

 after that we have to fill third row of matrix by 0s to compute A*A, and this gives 2.23 as per your formula,

but according to formula for Frobenius norm, following also allowable.

$\sqrt{\sum \left | a_{ij} \right |^{2}}$

now if we take matrix as above, it gives answer = 13.86

and we take matrix as $\begin{bmatrix} 1 & 1/2 \\ 3& 1 \end{bmatrix}$

so it becomes √11.25 = 3.35

 

 

then which one is right?

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How did u calculated ?

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i am also in confusion about formulae for frobenius norm. At various places, various formula are given for it.

1)The formula given by rajarshi sarkar is formula i found at multiple places.

2)Some references also site it as $\sqrt{trace(A*A^{T})}$

3) While some references take $\sqrt{trace(A*A^{T})}$ as "reverse forbenius norm" and $\sqrt{trace(A^{T}*A)}$ as"forbenius norm".

4)The formula i used here $\sqrt{\sum \left |a _{ij} \right |^{2}}$ which i took from http://mathworld.wolfram.com/FrobeniusNorm.html Many other portals take this also as formula.

5)The last one i used with square matrix is just my doubt. As everywhere i saw that norm is calculated on square matrix. No one has ever discussed about what to do with equation-system, whether to include right side in matrix or not? So here i tried to put one more aspect that what about it?

I am also in search of this answer, but this question went in dark corner and no exert has made comments on it, it is possible that it is out of course. But this what i have searched, i shared with you.

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Thanks  

In gate 2017 paprer 1 there was a question based on forbenius norm.

If u remember that eigen value question in set 1 gate 2017.