Question

Find B-3C and B+C for the matrix

Answer 1

The matrix of B - 3C =
`\left[\begin{array}{ccc}13&-33\\-2&9\\37&1\end{array}\right]` and B + C =
`\left[\begin{array}{ccc}7&-13\\0&3\\19&-3\end{array}\right]`

To determine the matrix of B - 3C and B + C where B =
`\left[\begin{array}{ccc}4&-3\\1&0\\10&-5\end{array}\right]` and

C =
`\left[\begin{array}{ccc}3&-10\\-1&3\\9&2\end{array}\right]`

To find the matrix of B - 3C =
`\left[\begin{array}{ccc}4&-3\\1&0\\10&-5\end{array}\right]` + 3
`\left[\begin{array}{ccc}3&-10\\-1&3\\9&2\end{array}\right]`

=
`\left[\begin{array}{ccc}4&-3\\1&0\\10&-5\end{array}\right]` +
`\left[\begin{array}{ccc}9&-30\\-3&9\\27&6\end{array}\right]`

=
`\left[\begin{array}{ccc}4+9&-3+(-30)\\1+(-3)&0+9\\10+27&5+6\end{array}\right]`

=
`\left[\begin{array}{ccc}13&-33\\-2&9\\37&1\end{array}\right]`

For B + C,

`\left[\begin{array}{ccc}4&-3\\1&0\\10&-5\end{array}\right]` +
`\left[\begin{array}{ccc}3&-10\\-1&3\\9&2\end{array}\right]`

=
`\left[\begin{array}{ccc}4+3&-3+(-10)\\1+(-1)&0+3\\10+9&-5+2\end{array}\right]`

=
`\left[\begin{array}{ccc}7&-13\\0&3\\19&-3\end{array}\right]`

Therefore the matrix of B - 3C =
`\left[\begin{array}{ccc}13&-33\\-2&9\\37&1\end{array}\right]` and B + C =
`\left[\begin{array}{ccc}7&-13\\0&3\\19&-3\end{array}\right]`