Question

Find the rank of matrix A

Answer 1

Answer:

You can think of an r x c matrix as a set of r row vectors, each having c elements; or you can think of it as a set of c column vectors, each having r elements.

The rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix or (b) the maximum number of linearly independent row vectors in the matrix. Both definitions are equivalent.

For an r x c matrix,

If r is less than c, then the maximum rank of the matrix is r.

If r is greater than c, then the maximum rank of the matrix is c.

The rank of a matrix would be zero only if the matrix had no elements. If a matrix had even one element, its minimum rank would be one.

Answer 2

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