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Magazine Problem 42
Give a geometric description of the span of the given vectors in the given space. \(\mathbf{v}_{1}=(2,-2)^{T}, \mathbf{v}_{2}=(2,-4)^{T}\), in \(\mathbf{R}^{2}\)
Problem 42
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrr}-1 & -9 & 10 \\ -7 & -19 & 26 \\ -2 & -10 & 12\end{array}\right)\)
Problem 43
Give a geometric description of the span of the given vectors in the given space. \(\mathbf{v}_{1}=(-1,3,3)^{T}, \mathbf{v}_{2}=(-3,-2,2)^{T}\), and \(\mathbf{v}_{3}=(4,-1,-5)^{T}\) in \(\mathbf{R}^{3}\)
Problem 43
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrr}1 & 0 & 4 \\ -3 & 3 & -2 \\ 4 & 0 & -2\end{array}\right)\)
Problem 44
Give a geometric description of the span of the given vectors in the given space. \(\mathbf{v}_{1}=(1,2,3)^{T}, \mathbf{v}_{2}=(2,4,6)^{T}\), and \(\mathbf{v}_{3}=(-5,-10,-15)^{T}\) in \(\mathbf{R}^{3}\)
Problem 44
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrr}1 & 2 & -3 \\ 0 & 6 & -2 \\ -2 & 3 & 2\end{array}\right)\)
Problem 45
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrr}0 & 1 & 2 \\ 2 & 0 & -2 \\ -1 & 0 & 3\end{array}\right)\)
Problem 46
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrrr}10 & -1 & -3 & 9 \\ 3 & 2 & -3 & 3 \\ 3 & 1 & -2 & 3 \\ -10 & 2 & 2 & -9\end{array}\right)\)
Problem 47
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrrr}3 & 0 & 20 & -8 \\ 2 & 3 & -2 & 0 \\ 6 & 4 & 17 & -8 \\ 16 & 10 & 50 & -23\end{array}\right)\)
Problem 48
Compute the determinant of the matrix. In each case, decide if there is a nonzero vector in the nullspace. \(\left(\begin{array}{rrrrrr}-120 & 60 & -79 & 52 & 68 & 123 \\ -262 & 162 & -216 & 124 & 184 & 262 \\ -142 & 78 & -100 & 64 & 92 & 142 \\ -262 & 162 & -216 & 124 & 184 & 262 \\ -10 & -4 & 6 & -2 & 2 & 10 \\ -112 & 60 & -79 & 52 & 68 & 115\end{array}\right)\)
