Respuesta :

keeping in mind that the element labeling is row,column, thus 2,1 simply means the 2nd row and 1st column, thus

[tex]\bf \stackrel{D}{ \begin{bmatrix} \boxed{}&\boxed{}&\boxed{}\\ d_{2,1}&d_{2,2}&d_{2,3}\\ \boxed{}&\boxed{}&\boxed{} \end{bmatrix}}+ \begin{bmatrix} 1&0&1\\-3&9&-7\\-20&2&4 \end{bmatrix}= \begin{bmatrix} 9&-3&2\\ 8&-1&0\\11&15&3 \end{bmatrix} \\\\\\ d_{2,1}+(-3)=8\implies \boxed{d_{2,1}=11} \\\\\\ d_{2,2}+9=-1\implies \boxed{d_{2,2}=-10} \\\\\\ d_{2,3}+(-7)=0\implies \boxed{d_{2,3}=7}\\\\ -------------------------------\\\\ 11+(-10)+7\implies 8[/tex]
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Using arithmetic operation, the missing row values of the matrix are 11, -10 and 7 respectively. Hence, the sum gives a value of 8

d21, d22, d23 refers to the values in the 2nd row of the matrix D.

Using the arithmetic operation to evaluate each value :

d21 + (-3) = 8

d21 - 3 = 8

d21 = 8 + 3

d21 = 11

d22 + 9 = - 1

d22 = - 1 - 9

d22 = - 10

d23 + (-7) = 0

d23 - 7 = 0

d23 = 0 + 7

d23 = 7

Therefore, the sum of d21, d22 and d23 is (11 + (-10) + 7) = 8

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