GATE CE 2014 Set 2 — Question 38
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Engineering Mathematics → Linear Algebra → Rank of a Matrix
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Question
The rank of the matrix is _______________
Correct answer
2 to 2
Solution
To find the rank of the matrix , we perform row operations to reach the row-echelon form.
Let be the rows of the matrix.
Observe that :
Since is a linear combination of and , the rows are linearly dependent. The rank is at most 2.
Checking and , they are clearly not multiples of each other, so they are linearly independent.
Therefore, the rank of the matrix is 2.
Let be the rows of the matrix.
Observe that :
Since is a linear combination of and , the rows are linearly dependent. The rank is at most 2.
Checking and , they are clearly not multiples of each other, so they are linearly independent.
Therefore, the rank of the matrix is 2.
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