Q: Find the matrix transpose of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]

\left[\begin{array}{ll}{\frac{\sqrt{2}}{2}}&{e^{4}}\\{2}&{8}\end{array}\right]

Q: Find the row echelon form of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]

\left[\begin{array}{ll}{\frac{\sqrt{2}}{2}}&{2}\\{0}&{8-2\sqrt{2}\times e^{4}}\end{array}\right]

Q: Find the reduced row echelon form of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]

\left[\begin{array}{ll}{1}&{0}\\{0}&{1}\end{array}\right]

Question 1

Evaluate the determinant of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

4\sqrt{2}-2e^{4}

Question 2

Find the matrix inverse of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

\left[\begin{array}{ll}{-\frac{8\sqrt{2}+4e^{4}}{e^{8}-8}}&{\frac{2\sqrt{2}+e^{4}}{e^{8}-8}}\{\frac{2\sqrt{2} imes e^{4}+e^{8}}{2e^{8}-16}}&{-\frac{4+\sqrt{2} imes e^{4}}{4e^{8}-32}}\end{array} ight]

Question 3

Find the matrix transpose of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

\left[\begin{array}{ll}{\frac{\sqrt{2}}{2}}&{e^{4}}\{2}&{8}\end{array} ight]

Question 4

Find the eigenvalues of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

\lambda_{1}=\frac{\sqrt{2}+16-\sqrt{258-32\sqrt{2}+32e^{4}}}{4},\lambda_{2}=\frac{\sqrt{2}+16+\sqrt{258-32\sqrt{2}+32e^{4}}}{4}

Question 5

Find the row echelon form of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

\left[\begin{array}{ll}{\frac{\sqrt{2}}{2}}&{2}\{0}&{8-2\sqrt{2} imes e^{4}}\end{array} ight]

Question 6

Find the reduced row echelon form of \left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25ight)}\{e^4}&  {8}\end{array}ight]

Accepted Answer

\left[\begin{array}{ll}{1}&{0}\{0}&{1}\end{array} ight]

[beginarrayl sin45^{circ} & log_5(25)e^4& 8endarray]

Matrices

Frequently Asked Questions

Evaluate the determinant of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)

Find the matrix inverse of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)

Find the matrix transpose of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)

Find the eigenvalues of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)

Find the row echelon form of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)

Find the reduced row echelon form of \(\left[\begin{array}{l} {\sin45^{\circ}} & {\log_5\left(25\right)}\\{e^4}& {8}\end{array}\right]\)