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Linear Algebra: Rank of Matrix Video Lecture | Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
FAQs on Linear Algebra: Rank of Matrix Video Lecture - Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
| 1. What is the rank of a matrix in linear algebra? |  |
Ans. The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It represents the dimension of the vector space spanned by its rows or columns.
| 2. How is the rank of a matrix related to its row and column space? | |
Ans. The rank of a matrix is equal to the dimension of both its row and column spaces. In other words, it tells us how many rows or columns are linearly independent and contribute to the space spanned by the matrix.
| 3. Can the rank of a matrix be greater than its number of rows or columns? | |
Ans. No, the rank of a matrix can never exceed the minimum of its number of rows or columns. If it did, it would mean that there are more linearly independent rows or columns than there are total rows or columns in the matrix, which is not possible.
| 4. How can the rank of a matrix be determined? | |
Ans. The rank of a matrix can be determined by performing row operations on the matrix and counting the number of non-zero rows in its row echelon form or reduced row echelon form. The number of non-zero rows is equal to the rank of the matrix.
| 5. Is the rank of a matrix affected by elementary row operations? | |
Ans. No, the rank of a matrix remains unchanged under elementary row operations. This property allows us to use row operations to simplify a matrix and determine its rank efficiently.
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