Answer:
The value of the entry represented by [tex]c_{41}[/tex] is 12.
Step-by-step explanation:
Let [tex]A = \left[\begin{array}{ccc}-5&3&8\\3&6&-5\\5&-9&0\\7&3&4\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}-7&-8&-5\\7&9&2\\2&5&-7\\2&8&-7\end{array}\right][/tex]. The sum of equal-sized matrices consist in the sum of each pair of corresponding elements. If [tex]C = (A-B)+A[/tex], then:
[tex]C = 2\cdot A -B[/tex] (1)
Then, [tex]c_{41}[/tex] is the element of matrix C located in the fourth row and first column and is defined by the following expression:
[tex]c_{41} = 2\cdot a_{41}-b_{41}[/tex] (2)
If we know that [tex]a_{41} = 7[/tex] and [tex]b_{41} = 2[/tex], then [tex]c_{41}[/tex] is:
[tex]c_{41} = 2\cdot (7)-2[/tex]
[tex]c_{41} = 12[/tex]
The value of the entry represented by [tex]c_{41}[/tex] is 12.
