a If A is a matrix with three rows and five columns then wha

(a) If A is a matrix with three rows and five columns, then what is the maximum possible number of leading 1’s in its reduced row echelon form?

(b) If B is a matrix with three rows and six columns, then what is the maximum possible number of parameters in the general solution of the linear system with augmented matrix B?

(c) If C is a matrix with five rows and three columns, then what is the minimum possible number of rows of zeros in any row echelon form of C?

Solution

(a)

If A is matrix with three rows and five columns , then its rank can not be more then 3.

So, the maximum number of leading1\'s in its reducedrow echelon form is 3.

(b)

If B is a matrix with three rows and six columns, its maximum is 3.

So, the maximum possible number of parameters inthe general solution of the linear systemwith augmented matrix is 3.

(c)

If C is a matrix with Five rows and three columns, its maximum rank is 3.

So, then minimum possible number of rows of zeros in any row echelon form of C is : 5-3=2