Question

Please help for 100 points.

Answer 1

By using matrix operations, the resulting matrix is $4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]$ is  $\left[\begin{array}{cc}3&6\\12&15\end{array}\right]$.

How to simplify a combination of matrices

In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:

$\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right]$

There are two fundamental operations for matrices:

Sum - The respective elements of the same row and the same column of the matrix are summed:

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]$

Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.

Scalar mutiplication - Every element of the matrix is multiplied by a scalar:

$2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]$

Where B(i, j) = k · A(i, j), k is the scalar.

Now we show the complete procedure to find the simplified expression:

$4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]$                         Given

$4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right]$               Definition of subtraction

$\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right]$                     Scalar multiplication

$\left[\begin{array}{cc}3&6\\12&15\end{array}\right]$                                             Sum of matrices / Result

The simplifed form of the matrix is $4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]$ is  $\left[\begin{array}{cc}3&6\\12&15\end{array}\right]$.

To learn more on matrices: brainly.com/question/9967572

#SPJ1