Question

(1 point) Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equivalent echelon form of matrix A is given to make your work easier. A = egin{bmatrix} 3 & 22 & 3 \ 2 & 1 & 0 \ -5 & -2 & 3 \ 2 & 7 & -1 \ -5 & 10 & 4 end{bmatrix} sim egin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \ 0 & 0 & 0 \ 0 & 0 & 0 end{bmatrix} Basis for the column space of A is left{ egin{bmatrix} 1 \ 0 \ 0 \ 0 \ 0 end{bmatrix}, egin{bmatrix} 0 \ 1 \ 0 \ 0 \ 0 end{bmatrix}, egin{bmatrix} 0 \ 0 \ 1 \ 0 \ 0 end{bmatrix} ight} Basis for the row space of A is

          (1 point) Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equivalent echelon form of matrix A is given to make your work easier.

A = egin{bmatrix} 3 & 22 & 3 \ 2 & 1 & 0 \ -5 & -2 & 3 \ 2 & 7 & -1 \ -5 & 10 & 4 end{bmatrix} sim egin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \ 0 & 0 & 0 \ 0 & 0 & 0 end{bmatrix}
Basis for the column space of A is
left{ egin{bmatrix} 1 \ 0 \ 0 \ 0 \ 0 end{bmatrix}, egin{bmatrix} 0 \ 1 \ 0 \ 0 \ 0 end{bmatrix}, egin{bmatrix} 0 \ 0 \ 1 \ 0 \ 0 end{bmatrix} 
ight}
Basis for the row space of A is

(1 point) Find bases for the column space, the row space, and the null space of matrix A. You should verify that the Rank-Nullity Theorem holds. An equivalent echelon form of matrix A is given to make your work easier.

A = eginbmatrix 3 22 3 2 1 0 -5 -2 3 2 7 -1 -5 10 4 endbmatrix sim eginbmatrix 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 endbmatrix
Basis for the column space of A is
left eginbmatrix 1 0 0 0 0 endbmatrix, eginbmatrix 0 1 0 0 0 endbmatrix, eginbmatrix 0 0 1 0 0 endbmatrix
ight
Basis for the row space of A is

Added by James D.

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