Problem 11
Find the determinant of the given matrix using cofactor expansion along any row or column you choose. \(\left[\begin{array}{cccc}-5 & -5 & 0 & -2 \\ 0 & 0 & 5 & 0 \\ 1 & 3 & 3 & 1 \\\ -4 & -2 & -1 & -5\end{array}\right]\)
Problem 11
Find the trace of the given matrix. \(\left[\begin{array}{cccc}-10 & 6 & -7 & -9 \\ -2 & 1 & 6 & -9 \\ 0 & 4 & -4 & 0 \\ -3 & -9 & 3 & -10\end{array}\right]\)
Problem 11
Find \(A^{T} ;\) make note if \(A\) is upper/lower triangular, diagonal, symmetric and/or skew symmetric. \(\left[\begin{array}{ccc}-9 & 4 & 10 \\ 6 & -3 & -7 \\ -8 & 1 & -1\end{array}\right]\)
Problem 12
Amatrix \(A\) is given. (a) Construct the submatrices used to compute the minors \(A_{1,1}, A_{1,2}\) and \(A_{1.3}\). (b) Find the cofactors \(C_{1,1}, C_{1,2},\) and \(C_{1,3}\) \(\left[\begin{array}{ccc}-6 & -4 & 6 \\ -8 & 0 & 0 \\ -10 & 8 & -1\end{array}\right]\)
Problem 12
Find \(A^{T} ;\) make note if \(A\) is upper/lower triangular, diagonal, symmetric and/or skew symmetric. \(\left[\begin{array}{ccc}4 & -5 & 2 \\ 1 & 5 & 9 \\ 9 & 2 & 3\end{array}\right]\)
Problem 12
Find the trace of the given matrix. \(\left[\begin{array}{cccc}5 & 2 & 2 & 2 \\ -7 & 4 & -7 & -3 \\ 9 & -9 & -7 & 2 \\ -4 & 8 & -8 & -2\end{array}\right]\)
Problem 12
Find the determinant of the given matrix using cofactor expansion along any row or column you choose. \(\left[\begin{array}{cccc}-1 & 0 & -2 & 5 \\ 3 & -5 & 1 & -2 \\ -5 & -2 & -1 & -3 \\ -1 & 0 & 0 & 0\end{array}\right]\)
Problem 12
Matrices \(A\) and \(\vec{b}\) are given. (a) Give \(\operatorname{det}(A)\) and \(\operatorname{det}\left(A_{i}\right)\) for all \(i\). (b) Use Cramer's Rule to solve \(A \vec{x}=\vec{b}\). If Cramer's Rule cannot be used to find the solution, then state whether or not a solution exists. \(A=\left[\begin{array}{ccc}-6 & -7 & -7 \\ 5 & 4 & 1 \\ 5 & 4 & 8\end{array}\right]\) \(\vec{b}=\left[\begin{array}{c}58 \\ -35 \\ -49\end{array}\right]\)
Problem 13
Find \(A^{T} ;\) make note if \(A\) is upper/lower triangular, diagonal, symmetric and/or skew symmetric. \(\left[\begin{array}{ccc}4 & 0 & -2 \\ 0 & 2 & 3 \\ -2 & 3 & 6\end{array}\right]\)
Problem 13
Find the determinant of the given matrix using cofactor expansion along any row or column you choose. \(\left[\begin{array}{lllll}4 & 0 & 5 & 1 & 0 \\ 1 & 0 & 3 & 1 & 5 \\ 2 & 2 & 0 & 2 & 2 \\ 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 2 & 5 & 3\end{array}\right]\)
