Help calculating sum of matrix elements

[frctl]

I wish to learn how to calculate the sum of matrix elements, according to the images I display below these questions I currently working on either use the sum symbol Σ or notation of the individual matrix elements.

Q1.

Here I am confused about which elements are being summed.

Q2.

Here I don't understand why the second element index position is a variable.
I know that the sigma above denotes 1 + 2 + 3 = 6 without considering a2,j.

Is someone able to guide me through understanding this concept better and how to arrive at the correct result? I currently don't find any detailed explanations in the lecture or textbook I am currently studying from.

 

[BigBeachBanana]

I wish to learn how to calculate the sum of matrix elements, according to the images I display below these questions I currently working on either use the sum symbol Σ or notation of the individual matrix elements.

Q1.
View attachment 35049
Here I am confused about which elements are being summed.

Q2.
View attachment 35050
Here I don't understand why the second element index position is a variable.
I know that the sigma above denotes 1 + 2 + 3 = 6 without considering a2,j.

Is someone able to guide me through understanding this concept better and how to arrive at the correct result? I currently don't find any detailed explanations in the lecture or textbook I am currently studying from.

In plain English, it's asking you to sum all the elements in row 2 with the column's index [imath]j = 1, 2, 3. [/imath]

[math]\sum_{j=1}^3 a_{2,j} = a_{2,1} + a_{2,2} + a_{2,3}[/math]

 

[Harry_the_cat]

Q1. Calculate A + 5I and then sum all the elements OR find the sum of the elements of A and add to the sum of the elements of 5I.

 

[frctl]

In plain English, it's asking you to sum all the elements in row 2 with the column's index [imath]j = 1, 2, 3. [/imath]

[math]\sum_{j=1}^3 a_{2,j} = a_{2,1} + a_{2,2} + a_{2,3}[/math]

Then the answer must be (6) + (5) + (4) = 15, correct?

Q1. Calculate A + 5I and then sum all the elements OR find the sum of the elements of A and add to the sum of the elements of 5I.

The sum of elements of A is every index element added together? What is 5I3 actually since there appears to be only one index element mentioned, I don't know which number in the matrix this is.

 

[blamocur]

What is 5I3 actually since there appears to be only one index element mentioned, I don't know which number in the matrix this is.

I believe [imath]I_3[/imath] refers to 3x3 identity matrix (https://en.wikipedia.org/wiki/Identity_matrix).

 

[stapel]

I wish to learn how to calculate the sum of matrix elements, according to the images I display below these questions I currently working on either use the sum symbol Σ or notation of the individual matrix elements.

Q1. What is the sum of the elements of the matrix [imath]A+5I_3[/imath], where [imath]A[/imath] is the following matrix?

[imath]A = \begin{bmatrix} 3&4&7 \\ 1&3&-2 \\ 4&6&9 \end{bmatrix}[/imath]

Here I am confused about which elements are being summed.

The elements being summed are the elements of the given matrix; namely, the matrix which is itself the sum of [imath]A[/imath] and [imath]5I_3[/imath]. So write down the identity matrix [imath]I_3[/imath], multiply it by 5, and add the two matrices, [imath]A[/imath] and [imath]5I_3[/imath].

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Q2. Given the following matrix:

[imath]A=\begin{bmatrix} 9&8&7 \\ 6&5&4 \\ 3&2&1 \end{bmatrix}[/imath]

Find the value of [imath]\displaystyle\sum_{j=1}^3 a_{2,j}[/imath].

Q2.
Here I don't understand why the second element index position is a variable.

The second element of the index stands for the column of the entry. The first element of the index stands for the row of the entry.

So fixing the first element means that the row will always be the same. Letting the second element change (from 1 to 2 to 3) means that you're summing the values from all of the column values that are in the second row.

Eliz.