(A) The trace of a square matrix is defined as the sum of its principal diagonal elements. Given the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 &

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(A) The trace of a square matrix is defined as the sum of its principal diagonal elements. Given the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$. The diagonal elements are $a_{11} = 1$,$a_{22} = 7$,and $a_{33} = 9$. The trace $tr(A) = a_{11} + a_{22} + a_{33}$. $tr(A) = 1 + 7 + 9 = 17$. Therefore,the trace of the matrix is $17$.

Class 12 Mathematics 3-4. Matrices and Determinants Special types of matrices, Transpose of matrices and Trace of matrices

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The trace of the matrix $A = \begin{bmatrix} 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$ is defined only for square matrices. If we consider the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$,what is its trace?

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A
$17$
B
$25$
C
$3$
D
$12$

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3-4. Matrices and Determinants

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Special types of matrices, Transpose of matrices and Trace of matrices

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The trace of the matrix $A = \begin{bmatrix} 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$ is defined only for square matrices. If we consider the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$,what is its trace?

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For the matrices $A$ and $B$,verify that $(AB)^{\prime} = B^{\prime} A^{\prime}$ where $A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix}$.

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