Basic Maths - Grand Test 1 -Q7

+2 votes

Rank of the following matrix is ____

                                                     \begin{bmatrix} 6 & 4& 10 & 16 \\ 1 & 2 & 3 & 4\\ 3 & 6 & 9 & 12\\ 8 & -1 & 7 & 15 \end{bmatrix}

(A). 4

(B). 3

(C). 2

(D). 1

asked Jun 21 in Basic Maths by gbeditor (4,380 points)
reshown Jun 23 by gbeditor

2 Answers

+1 vote
 
Best answer

Applying R_2\rightarrow 6R_2-R_1;R_3\rightarrow 2R_3-R_1;R_4\rightarrow 6R_4-8R_1;

                                             \begin{bmatrix} 6 &4 &10 &16 \\ 0& 8 &8 &8 \\ 0& 8 &8 &8 \\ 0& -38 &-38 &-38 \end{bmatrix}

R_3\rightarrow R_3-R_2;R_4\rightarrow 8R_4-38R_2;

                                         \begin{bmatrix} 6 &4 &10 &16 \\ 0& 8 &8 &8 \\ 0& 0 &0 &0 \\ 0& 0 &0 &0 \end{bmatrix} \rightarrow \text{Echelon form}

Rank = no. of nonzero rows = 2

answered Jun 24 by gbeditor (4,380 points)
Sir please clear this doubt. I have read that when rows or columns are proportional then rank of the matrix is equal to 1. This means each and every row or column should be proportional to each other? Because i mislead this question by seeing that R2 and R3 are proportional and marked ans as 1.
can u give reference of that as well as, please tell which rows or column u r talking about.
1 2 3 |  Sorry, i misunderstood the concept and realized now that every row should       
2 4 6 |  be proportional then only rank=1 possible.
3 6 9 |
0 votes
C is correct one rank is 2
answered Jun 23 by tsnikhilsharmagate2018 (17,270 points)
Answer:
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