ii. Truncate to; a. 2 decimal places b. Whole number State the type of matrix \( P \) and matrix \( Q \), giving a reason for your answer. \[ \begin{array}{rll}6 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array} \text { and } Q=\begin{array}{llll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array} \]

To truncate the matrices \( P \) and \( Q \) to the specified formats, we first need to identify the matrices: 1. **Matrix \( P \)**: \[ P = \begin{bmatrix} 6 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{bmatrix} \] 2. **Matrix \( Q \)**: \[ Q = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix} \] ### Truncation **a. Truncate to 2 decimal places:** Since all the entries in both matrices are whole numbers, truncating to 2 decimal places will not change the values. Thus, the truncated matrices are: \[ P = \begin{bmatrix} 6.00 & 0.00 & 0.00 \\ 0.00 & 4.00 & 0.00 \\ 0.00 & 0.00 & 1.00 \end{bmatrix} \] \[ Q = \begin{bmatrix} 5.00 & 0.00 & 0.00 \\ 0.00 & 5.00 & 0.00 \\ 0.00 & 0.00 & 5.00 \end{bmatrix} \] **b. Truncate to whole number:** Again, since all entries are already whole numbers, truncating to whole numbers will not change the values. Thus, the truncated matrices remain: \[ P = \begin{bmatrix} 6 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{bmatrix} \] \[ Q = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix} \] ### Type of Matrices **Matrix \( P \)**: - **Type**: Diagonal Matrix - **Reason**: A diagonal matrix is a square matrix in which all the entries outside the main diagonal are zero. In matrix \( P \), the only non-zero entries are on the main diagonal (6, 4, and 1). **Matrix \( Q \)**: - **Type**: Scalar Matrix - **Reason**: A scalar matrix is a special case of a diagonal matrix where all the diagonal elements are the same. In matrix \( Q \), all diagonal entries are equal to 5, and all off-diagonal entries are zero. In summary: - Matrix \( P \) is a diagonal matrix. - Matrix \( Q \) is a scalar matrix.