Question

Amjad thought two number whose sum is 12 and whose difference is 4. Find the number( use matrix method only)

Answer 1

Let's represent the two numbers as a column vector:

\[ A = \begin{bmatrix} x \\ y \end{bmatrix} \]

The sum of the numbers is 12, so we have the equation:

\[ x + y = 12 \]

The difference between the numbers is 4, so:

\[ x - y = 4 \]

We can represent these equations as a matrix equation:

\[ \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 12 \\ 4 \end{bmatrix} \]

Now, we can use matrix inversion to solve for the vector \([x, y]\). The solution will give you the values of the two numbers Amjad is thinking of.