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Question

The rank of the matrix ⎡⎢⎣3−12−312−624⎤⎥⎦ is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2

The rank of a matrix is simply the maximum number of linearly independent vectors in a matrix. And this number is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows. So, first step would be to convert the given matrix into row echelon form.

R2R2+R1 and R3R3+2R1

312004008

R1R113, R2R2(14) and R3R3(18)

⎢ ⎢31323001001⎥ ⎥

R3R3R2

⎢ ⎢11323001000⎥ ⎥

We have 2 non zero rows Rank = 2.


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