CadyMath

#1. \(A=\begin{bmatrix} -6 & -9\\-7 & -9\\-6 & -1\\\end{bmatrix}\)

\( C(A)=\Reals^4 \).

\(C(A)\) is a plane in 3-space.

\(C(A)\) is a plane in 4-space.

\(C(A)\) only contains the zero vector.

#2. \(A=\begin{bmatrix} 2 & -7 & 2 & 3\\-10 & -3 & 5 & -1\\\end{bmatrix}\)

\( C(A)=\Reals^2 \).

\( C(A)=\Reals^4 \).

\(C(A)\) is a plane in 3-space.

\(C(A)\) only contains the zero vector.

#3. \(A=\begin{bmatrix} 1 & 7 & 40\\-7 & 1 & -30\\9 & 1 & 50\\\end{bmatrix}\)

\( N(A)=\Reals^3 \).

\(N(A)\) is a line in 2-space.

\(N(A)\) is a line in 3-space.

\(N(A)\) is a plane in 4-space.

#4. \(A=\begin{bmatrix} -4 & 4 & -16\\-2 & -4 & -2\\-8 & 7 & -31\\\end{bmatrix}\)

\( N(A)=\Reals^4 \).

\(N(A)\) is a line in 2-space.

\(N(A)\) is a line in 3-space.

\(N(A)\) is a plane in 4-space.

#5. \(A=\begin{bmatrix} 1 & 1\\4 & -4\\7 & 3\\7 & -5\\\end{bmatrix}\)

\( C(A^T)=\Reals^2 \).

\(C(A^T)\) is a line in 2-space.

\(C(A^T)\) is a plane in 4-space.

\(C(A^T)\) is a three-dimensional space within 4-space.

#6. \(A=\begin{bmatrix} -7 & -3\\6 & -7\\10 & 4\\\end{bmatrix}\)

\( C(A^T)=\Reals^2 \).

\( C(A^T)=\Reals^3 \).

\( C(A^T)=\Reals^4 \).

\(C(A^T)\) is a line in 4-space.

#7. \(A=\begin{bmatrix} 2 & 3\\-9 & 2\\-3 & 9\\6 & 4\\\end{bmatrix}\)

\( N(A^T)=\Reals^4 \).

\(N(A^T)\) is a plane in 3-space.

\(N(A^T)\) is a plane in 4-space.

\(N(A^T)\) is a three-dimensional space within 4-space.

#8. \(A=\begin{bmatrix} -5 & -4\\9 & 5\\6 & -10\\1 & 5\\\end{bmatrix}\)

\( N(A^T)=\Reals^2 \).

\( N(A^T)=\Reals^4 \).

\(N(A^T)\) is a line in 2-space.

\(N(A^T)\) is a plane in 4-space.

#9. \(A=\begin{bmatrix} -1 & -4\\-4 & 1\\4 & -4\\10 & 7\\\end{bmatrix}\)

\(1\)

\(2\)

\(3\)

\(4\)

#10. \(A=\begin{bmatrix} -2 & 6\\-1 & -6\\4 & 5\\-2 & 8\\\end{bmatrix}\)

\(0\)

\(1\)

\(2\)

\(3\)