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Rank of Matrix

Lecture on Rank
Content covered: 

The concept of Rank of Matrix

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Lecture on Finding Rank of Matrix
Content covered: 

Step by step procedure to find rank

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Find the value of \(a\) and  \(b\)such that the rank of matrix \(A= \begin{bmatrix} 1 & -2 & 3 &1\\ 2 & 1 & -1 & 2\\ 6 & -2 & a & b\\ \end{bmatrix}\)is 

(i)    3

(ii)    2

GATE 1994 Example on Rank of Matrix

The rank of matric  \(\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1\\ \end{bmatrix}\)is :

a) 0

b) 1

c) 2

d) 3

Things you need to know

The rank of a matrix is the maximum number of independent rows (or, the maximum number of independent columns).

 

Now,

if we observe, then the column vector \(\begin{bmatrix} 0 \\ 9 \\ 1 \end{bmatrix}\) is a multiple of  \(\begin{bmatrix} 0 \\ 3 \\ 1 \end{bmatrix}\)

Therefore, The total number of linearly independent column vectors = 2

Hence, Rank = 2 .

 

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  • This quiz contains 10 questions on the topic Determinants and Matrices​
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Difficulty Level:  intermediate