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For following matrix, which of the options is/are true?

A= 3 1 4

     0 5 8

    -3 4 4

    1 2 4

a:) Rank of Transpose of A is 4

b:) Rank(A)=3

c:) Linearly independent row vectors =2

d:) Matrix a is linearly independent

e:) Maximum linearly independent tuples are 3

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Ans :  c,d
The rank of matrix is equal to the rank of transpose of a matrix.
Here Rank =2 (Using Echelon method ) . So, option a , b is eliminated .
No of linearly independent solutions =(n-r) where n is no of variable and r is rank of matrix .So, here it is 4-2=2.
So, c,d is correct and e is eliminated.
Hope it helps.
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