Linear AlgebraTranspose And Trace Of A Matrix Problems 1

Ex:1

$$A=\left(\begin{array}{lll}{1} & {2} & {9} \\ {3} & {4} & {8} \\ {5} & {6} & {7}\end{array}\right)$$

$$\Rightarrow A^{T}=\left(\begin{array}{lll}{1} & {3} & {5} \\ {2} & {4} & {6} \\ {9} & {8} & {7}\end{array}\right)$$

Ex:2

$$B=\left[\begin{array}{lll}{1} & {6} & {2} \\ {3} & {9} & {4}\end{array}\right]$$

$$B^{T}=\left(\begin{array}{ll}{1} & {3} \\ {6} & {9} \\ {2} & {4}\end{array}\right)$$

Ex:1

$$A=\left(\begin{array}{lll}{1} & {2} & {5} \\ {2} & {4} & {6} \\ {5} & {6} & {7}\end{array}\right)$$

$$\Rightarrow tr(A)=1+4+7=12$$