Matrix A has full rank ifa.determinant of A is positiveb.rows of Matrix A are linearly dependentc.determinant of A is negatived.columns of Matrix A are linearly dependent

The determinant rank of an 𝑚×𝑛 matrix A is equal to the ___ of A

The rank of a matrix is always less than or equal to:a.The maximum element in the matrixb.The sum of the elements in the matrixc.The minimum element in the matrixd.The smaller of the number of rows and columns of the matrix

Let A and B be n × p matrix respectively and p × q matrix and defineC = AB. Prove the following statements.(a) If the columns of B are linearly dependent, then the columns of C are linearlydependent.(b) If the rows of A are linearly dependent, then the rows of C are linearly depen-dent.

Use the fact that matrices A and B are row-equivalent.A = −2 −5 8 0 −17 1 3 −5 1 5−5 −9 13 7 −671 7 −13 5 −3B = 1 0 1 0 1 0 1 −2 0 30 0 0 1 −50 0 0 0 0(a) Find the rank and nullity of A.rank nullity

If 0 is an Eigen value of a matrix A, then the set of columns of A isQuestion 5Select one:Linearly independent always.Linearly independent or linearly dependent..Cannot be determined.Linearly dependent always.