State the type of matrix P and matrix Q, giving a reason for your answer. (4 Marks $$ \begin{array}{rrr}6 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 1\end{array} \text { and } \mathrm{Q}=\begin{array}{rrr}5 & 0 & 0 \ 0 & 5 & 0 \ 0 & 0 & 5\end{array} $$

Question

UpStudy AI · Accepted Answer

Matrix $$ P $$ is a diagonal matrix because all its non-zero entries are on the main diagonal. Matrix $$ Q $$ is a scalar matrix because all its diagonal entries are the same and equal to 5. To determine the type of matrices $$ P $$ and $$ Q $$, we can analyze their structure and properties. 1. **Matrix $$ P $$**: $$ P = \begin{pmatrix} 6 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 1 \end{pmatrix} $$ - **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), and all other entries are zero. 2. **Matrix $$ Q $$**: $$ Q = \begin{pmatrix} 5 & 0 & 0 \ 0 & 5 & 0 \ 0 & 0 & 5 \end{pmatrix} $$ - **Type**: Scalar Matrix - **Reason**: A scalar matrix is a special type of diagonal matrix where all the diagonal elements are the same. In matrix $$ Q $$, all the diagonal entries are equal to 5, and all off-diagonal entries are zero. Therefore, it is a scalar matrix. In summary: - Matrix $$ P $$ is a **diagonal matrix**. - Matrix $$ Q $$ is a **scalar matrix**.

State the type of matrix P and matrix Q, giving a reason for your answer. (4 Marks \[ \begin{array}{rrr}6 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array} \text { and } \mathrm{Q}=\begin{array}{rrr}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array} \]

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

State the type of matrix P and matrix Q, giving a reason for your answer. (4 Marks \[ \begin{array}{rrr}6 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1\end{array} \text { and } \mathrm{Q}=\begin{array}{rrr}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array} \]

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions