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The Four Fundamental Subspaces QuizName __________

Describe the column space \(C(A)\) of \(A\).

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

State the dimension of the column space \(C(A)\) of \(A\).

#2. \(A=\begin{bmatrix} 3 & 1\\5 & 8\\\end{bmatrix}\)

Describe the left null space \(N(A^T)\) of \(A\).

#3. \(A=\begin{bmatrix} 6 & -5 & 8 & -3\\7 & -2 & -3 & 6\\\end{bmatrix}\)

State the dimension of the left null space \(N(A^T)\) of \(A\).

#4. \(A=\begin{bmatrix} 1 & 6\\6 & 36\\\end{bmatrix}\)

Describe the row space \(C(A^T)\) of \(A\).

#5. \(A=\begin{bmatrix} -1 & 7\\-6 & 6\\-4 & 5\\-8 & -2\\\end{bmatrix}\)

State the dimension of the row space \(C(A^T)\) of \(A\).

#6. \(A=\begin{bmatrix} 2 & -6 & 5\\6 & -4 & 9\\-7 & -1 & 1\\\end{bmatrix}\)

Describe the null space \(N(A)\) of \(A\).

#7. \(A=\begin{bmatrix} -1 & -9\\6 & 1\\2 & 2\\10 & 3\\\end{bmatrix}\)

State the dimension of the null space \(N(A)\) of \(A\).

#8. \(A=\begin{bmatrix} 9 & 2\\-1 & -2\\-10 & -5\\6 & 5\\\end{bmatrix}\)

Determine the rank of \(A\).

#9. \(A=\begin{bmatrix} 3 & -3\\8 & 8\\-4 & 4\\3 & -2\\\end{bmatrix}\)
#10. \(A=\begin{bmatrix} 9 & 2 & 7\\-3 & 4 & 3\\\end{bmatrix}\)
 1
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 2
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 3
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 4
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 5
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 8
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 9
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10
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