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Question

312312624What is the rank of the matrix.


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 R3R3+2R1

312004008

R1R113, R2R2(14), R3R3(18)

⎢ ⎢31323001001⎥ ⎥

R3R3R2

⎢ ⎢11323001000⎥ ⎥

we have 2 non zero rows Rank = 2.


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