Question

If matrix C represents (A-B)+A, the value of the entry represented by C41 is

Answer 1

Answer:

The value of the entry represented by $c_{41}$ is 12.

Step-by-step explanation:

Let $A = \left[\begin{array}{ccc}-5&3&8\\3&6&-5\\5&-9&0\\7&3&4\end{array}\right]$ and $B = \left[\begin{array}{ccc}-7&-8&-5\\7&9&2\\2&5&-7\\2&8&-7\end{array}\right]$. The sum of equal-sized matrices consist in the sum of each pair of corresponding elements. If $C = (A-B)+A$, then:

$C = 2\cdot A -B$ (1)

Then, $c_{41}$ is the element of matrix C located in the fourth row and first column and is defined by the following expression:

$c_{41} = 2\cdot a_{41}-b_{41}$ (2)

If we know that $a_{41} = 7$ and $b_{41} = 2$, then $c_{41}$ is:

$c_{41} = 2\cdot (7)-2$

$c_{41} = 12$

The value of the entry represented by $c_{41}$ is 12.