ISRO2014-72

Question

The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$  is ______ .

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Comments

tell if any mistake there in matrix. i will edit and post answer.

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$\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ check it now.

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ccorrect

Answer 1

Rank of Matrix is 2.

That's 2.

Comments

please explain it

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Check gupta ji.

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how you decide its rank 2.

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count rows which are non -zero ,here is 2.

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Why didn't we further tried to reduced it? Why we stopped ?

I mean maybe we could have reduced it to 1

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Read this;

https://en.wikipedia.org/wiki/Row_echelon_form

http://stattrek.com/matrix-algebra/matrix-rank.aspx

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means, if we get row echelon form we stop.

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can u elaborate what is ROW ECHELON FORM ? I need to know when we need to stop?

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https://www.youtube.com/watch?v=24Jin6qm05o

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@ cse7 .Check this lecture.

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are you sure that once you once you find  ROW ECHELON FORM no need to reduce further??

Answer 2

R3 + 2R1 and then R3-R2. We get last row as zero. Hence, rank is 2.