Respuesta :
Answer:
[tex]\therefore A^{T}=\frac{2}{3} \left[\begin{array}{cc}-4&8\\-5&4\\8&-8\end{array}\right][/tex]
Step-by-step explanation:
Matrix transpose :The matrix transpose is switches the rows and column elements.
If a constant term multiplies with a matrix , then the constant term will multiply each element of the matrix.
Given
[tex]A=\frac{2}{3} \left[\begin{array}{ccc}-4&-5&8\\8&4&-8\end{array}\right][/tex]
[tex]=\left[\begin{array}{ccc}\frac{2}{3} .(-4)&\frac{2}{3}(-5)&\frac{2}{3}8\\ \\ \frac{2}{3}.8&\frac{2}{3}.4&\frac{2}{3}.(-8)\end{array}\right][/tex]
[tex]=\left[\begin{array}{ccc}\frac{-8}{3} &\frac{-10}{3}&\frac{16}{3}\\\ \\ \frac{16}{3}&\frac{8}{3}&\frac{-16}{3}\end{array}\right][/tex]
[tex]A^{T}=\left[\begin{array}{cc}\frac{-8}{3} &\frac{16}{3}\\\ \\ \frac{-10}{3}&\frac{8}{3}\\ \\ \frac{16}{3}&\frac{-16}{3}\end{array}\right][/tex]
[tex]=\frac{2}{3} \left[\begin{array}{cc}-4&8\\-5&4\\8&-8\end{array}\right][/tex]
[tex]\therefore A^{T}=\frac{2}{3} \left[\begin{array}{cc}-4&8\\-5&4\\8&-8\end{array}\right][/tex]
