Let A be the matrix -3 2 2 -3 -6 -6 -7 3 -12 0 4 26 -9 -10 -12 -3 1. A basis for

Question

Let A be the matrix -3 2    2   -3 -6 -6 -7   3 -12 0 4   26 -9   -10 -12 -3 1. A basis for the row space of A is___________     Are the row vectors of A linearlyindependent? 2. The rank of A is_________ and the nullity of Ais_________     Is the row space of A equal toR4?     Does the system Ax =0 have only the trivial solution?     Is the matrix A invertible? 3. A basis for the column space of A is_________    Are the column vectors of A linearlyindependent?    The rank of AT is ________and thenullity of AT is__________ 4. Is the column space of A equal toR4?     Does the systemATx = 0 have only thetrivial solution?     Is the matrix ATinvertible? Let A be the matrix -3 2    2   -3 -6 -6 -7   3 -12 0 4   26 -9   -10 -12 -3 1. A basis for the row space of A is___________     Are the row vectors of A linearlyindependent? 2. The rank of A is_________ and the nullity of Ais_________     Is the row space of A equal toR4?     Does the system Ax =0 have only the trivial solution?     Is the matrix A invertible? 3. A basis for the column space of A is_________    Are the column vectors of A linearlyindependent?    The rank of AT is ________and thenullity of AT is__________ 4. Is the column space of A equal toR4?     Does the systemATx = 0 have only thetrivial solution?     Is the matrix ATinvertible?

Explanation / Answer

1. (1,0,9/2,0,25/4),(0,1,-4,0,-3),(0,0,0,1,-1/2)      Yes

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