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Magazine Problem 53
Parameterize the equation of the line given in standard form. $$ 2 x+y-3=0 $$
Problem 54
In Problems , find the eigenvalues \(\lambda_{1}\) and \(\lambda_{2}\) and corresponding eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) for each matrix A. Determine the equations of the lines through the origin in the direction of the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\), and graph the lines together with the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) and the vectors \(A \mathbf{v}_{1}\) and \(A \mathbf{v}_{2}\). $$ A=\left[\begin{array}{rr} 3 & 6 \\ -1 & -4 \end{array}\right] $$
Problem 54
Use the determinant to determine whether the matrix $$ A=\left[\begin{array}{rr} -1 & 3 \\ 0 & 3 \end{array}\right] $$ is invertible.
Problem 54
Parameterize the equation of the line given in standard form. $$ x-5 y+7=0 $$
Problem 55
In Problems , find the eigenvalues \(\lambda_{1}\) and \(\lambda_{2}\) and corresponding eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) for each matrix A. Determine the equations of the lines through the origin in the direction of the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\), and graph the lines together with the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) and the vectors \(A \mathbf{v}_{1}\) and \(A \mathbf{v}_{2}\). $$ A=\left|\begin{array}{ll} 2 & 1 \\ 2 & 3 \end{array}\right| $$
Problem 55
In Problems \(55-58\), find the parametric equation of the line in \(x-\) \(y-z\) space that goes through the indicated point in the direction of the indicated vector. $$ (1,-1,2),\left[\begin{array}{r} 1 \\ -2 \\ 1 \end{array}\right] $$
Problem 55
Use the determinant to determine whether the matrix $$ A=\left[\begin{array}{ll} 4 & -1 \\ 8 & -2 \end{array}\right] $$ is invertible.
Problem 56
Use the determinant to determine whether the matrix $$ A=\left[\begin{array}{ll} -1 & 2 \\ -1 & 2 \end{array}\right] $$ is invertible.
Problem 56
Find the parametric equation of the line in \(x-\) \(y-z\) space that goes through the indicated point in the direction of the indicated vector. $$ (2,0,4),\left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right] $$
Problem 56
In Problems , find the eigenvalues \(\lambda_{1}\) and \(\lambda_{2}\) and corresponding eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) for each matrix A. Determine the equations of the lines through the origin in the direction of the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\), and graph the lines together with the eigenvectors \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2}\) and the vectors \(A \mathbf{v}_{1}\) and \(A \mathbf{v}_{2}\). $$ A=\left[\begin{array}{rr} -3 & -0.5 \\ 7 & 1.5 \end{array}\right] $$
