The matrix \(\mathbf { P }\) is given by \(\mathbf { P } = \left( \begin{array} { l l l l } 1 & 0 & - 2 & 2 4 & 2 & - 2 & 3 \end{array} \right)\).
Write down the dimensions of \(\mathbf { P }\).
Write down the transpose of \(\mathbf { P }\).
The matrices \(\mathbf { Q } , \mathbf { R }\) and \(\mathbf { S }\) are given by \(\mathbf { Q } = \left( \begin{array} { l l } 1 & 2 \end{array} \right) , \mathbf { R } = \left( \begin{array} { r r } 3 & - 4 2 & 3 \end{array} \right)\) and \(\mathbf { S } = \left( \begin{array} { l l } 3 & - 2 \end{array} \right)\).
Write down the sum of the two of these matrices which are conformable for addition.
The dimensions of matrix \(\mathbf { A }\) are 4 by 5. The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are conformable for multiplication so that the matrix \(\mathbf { C } = \mathbf { B A }\) can be formed. The matrix \(\mathbf { C }\) has 6 rows.
Write down the number of columns that \(\mathbf { C }\) has.
Write down the dimensions of \(\mathbf { B }\).
Explain whether the matrix \(\mathbf { A B }\) can be formed.
Find the value of \(c\) for which \(\left( \begin{array} { r r } - 2 & 3 6 & 10 \end{array} \right) \left( \begin{array} { r r } c & 5 10 & 13 \end{array} \right) = \left( \begin{array} { r r } c & 5 10 & 13 \end{array} \right) \left( \begin{array} { r r } - 2 & 3 6 & 10 \end{array} \right)\).