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I see that you've uploaded an image with several matrix-related questions. I'll go through each of them one by one and provide solutions.

### 1. If matrix A = \(\begin{pmatrix} 2 & 0 \\ 3 & 4 \end{pmatrix}\) and matrix B = \(\begin{pmatrix} 6 & 2 \\ -1 & 9 \end{pmatrix}\), what is the value of \(A + B^T\)?

We need to first find the transpose of matrix \(B\) and then add it to matrix \(A\).

Transpose of \(B\), \(B^T = \begin{pmatrix} 6 & -1 \\ 2 & 9 \end{pmatrix}\).

Now, adding matrices \(A\) and \(B^T\):
\[
A + B^T = \begin{pmatrix} 2 & 0 \\ 3 & 4 \end{pmatrix} + \begin{pmatrix} 6 & -1 \\ 2 & 9 \end{pmatrix} = \begin{pmatrix} 8 & -1 \\ 5 & 13 \end{pmatrix}
\]

So, \(A + B^T = \begin{pmatrix} 8 & -1 \\ 5 & 13 \end{pmatrix}\).

### 2. Matrix \(P = \begin{pmatrix} -2 & 0 & 2 \\ 0 & -3 & 4 \\ 0 & 0 & 6 \end{pmatrix}\). What is the determinant of matrix \(P\)?

Matrix \(P\) is a triangular matrix (lower triangular matrix), so its determinant is the product of the diagonal elements:
\[
\text{det}(P) = (-2) \times (-3) \times 6 = 36
\]

So, the determinant of \(P\) is 36.

### 3. Give an example of a diagonal matrix.

A diagonal matrix is a square matrix in which all off-diagonal elements are zero. An example could be:
\[
D = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 

Jika matriks A = \(\begin{pmatrix} 2 & 0 \\ 3 & 4 \end{pmatrix}\) dan matriks B = \(\begin{pmatrix} 6 & 2 \\ -1 & 9 \end{pmatrix}\), maka berapakah nilai dari A + B^T? Simpulkan nilai dari determinan matriks P, Buatlah contoh matriks diagonal, simpulkanlah nilai dari invers matriks Q, dan analisislah matriks persamaan \((a-2b)/(3b) = (1/6)\).

Learn how to perform matrix operations, including transpose, determinants, and inverses, with step-by-step solutions. We solve for A + B^T, find the determinant of matrix P, give examples of diagonal matrices, and more.

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