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