Help with a strange symbol

M

MathStudent1999

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Mar 18, 2012
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76
............(1 2)............... (5 6)............... (9 10) ................ (13 14)
If S1 = (3 4) and S2 = (7 8) and S3 = (11 12) and S4 = (15 16)

(The brackets are joined, it's supposed to be one big bracket)(Ignore the periods)

What is the sum of the entries in Sk? Express your answer in terms of k.

I do not know what (1 2) means.
................................(3 4)
 
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MathStudent1999 said:
............(1 2)............... (5 6)............... (9 10) ................ (13 14)
If S1 = (3 4) and S2 = (7 8) and S3 = (11 12) and S4 = (15 16)

(The brackets are joined, it's supposed to be one big bracket)(Ignore the periods)

What is the sum of the entries in Sk? Express your answer in terms of k.

I do not know what (1 2) means.
................................(3 4)
Click to expand...

Matrix ?
 
MathStudent1999 said:
............(1 2)............... (5 6)............... (9 10) ................ (13 14)
If S1 = (3 4) and S2 = (7 8) and S3 = (11 12) and S4 = (15 16)

(The brackets are joined, it's supposed to be one big bracket)(Ignore the periods)

What is the sum of the entries in Sk? Express your answer in terms of k.

I do not know what (1 2) means.
................................(3 4)
Click to expand...
I am having trouble understanding your question. What brackets are joined, what periods are to be ignored.
.
\(\displaystyle S_1= \{3, 4\}\ and\ S_2 = \{7, 8\}\ and\ S_3 = \{11, 12\}\ and\ S_4 = \{15, 16\}.\) Is that what you are given?
.

In that case, \(\displaystyle S_k\ means\ S_1\ if\ k = 1, S_2\ if\ k = 2, and\ so\ on.\)
.
k is an index that distinguishes between the four different sets that you are given. If I understand the question, you are being asked to find a formula that describes the members of set k. In other words, you are being asked to replace the four definitions of sets that use numbers with a single definition that uses the letter k as a variable. Then you are to express the sum of the members of set k in terms of k.

 
JeffM said:
I am having trouble understanding your question. What brackets are joined, what periods are to be ignored.
.
\(\displaystyle S_1= \{3, 4\}\ and\ S_2 = \{7, 8\}\ and\ S_3 = \{11, 12\}\ and\ S_4 = \{15, 16\}.\) Is that what you are given?
.

In that case, \(\displaystyle S_k\ means\ S_1\ if\ k = 1, S_2\ if\ k = 2, and\ so\ on.\)
.
k is an index that distinguishes between the four different sets that you are given. If I understand the question, you are being asked to find a formula that describes the members of set k. In other words, you are being asked to replace the four definitions of sets that use numbers with a single definition that uses the letter k as a variable. Then you are to express the sum of the members of set k in terms of k.
Click to expand...

---->(1 2)<---- This brackets are joined.
---->(3 4)<----

........................... <---- The random periods separating (1 2), (5 6), (9 10) and (13 14) should be ignored. They are just there because the spaces kept on disappearing. I think it is matrix, but it is ( instead of [.
 
MathStudent1999 said:
---->(1 2)<---- This brackets are joined.
---->(3 4)<----

........................... <---- The random periods separating (1 2), (5 6), (9 10) and (13 14) should be ignored. They are just there because the spaces kept on disappearing. I think it is matrix, but it is ( instead of [.
Click to expand...
As princeps observes, these are matrices .. 2×2 square matrices, so each has four elements.

\(\displaystyle \displaystyle S_1 = \begin{pmatrix} 1 & 2 \\3 & 4 \end{pmatrix} ,\;\;S_2 = \begin{pmatrix} 5 & 6 \\7 & 8 \end{pmatrix},\;\;\) etc.
 
[ (2K^2 - K) (2K^2)] <----- This is what I got. I'm not very good with matrices. Is the the
[ (2K^2 + K) (2K^2 +2k)] simplest form?
 
MathStudent1999 said:
[ (2K^2 - K) (2K^2)] <----- This is what I got. I'm not very good with matrices. Is the the
[ (2K^2 + K) (2K^2 +2k)] simplest form?
Click to expand...
Did you check your work?\(\displaystyle \ For\ S_2,\ e_{1,1} = (2 * 2^2) - 2 = (2 * 4) - 2 = 8 - 2 = 6 ≠ 5.\)
.
\(\displaystyle For\ S_2,\ e_{1,2} = 2 * 2^2 = 2 * 4 = 8 ≠ 6.\)
.
\(\displaystyle For\ S_2,\ e_{2,1} = (2 * 2^2) + 2 = 8 + 2 = 10 ≠ 7.\)
.
\(\displaystyle For\ S_2,\ e_{2,2} = (2 * 2^2) + (2 * 2) = 8 + 4 = 12 ≠ 9.\)
 
JeffM said:
Did you check your work?\(\displaystyle \ For\ S_2,\ e_{1,1} = (2 * 2^2) - 2 = (2 * 4) - 2 = 8 - 2 = 6 ≠ 5.\)
.
\(\displaystyle For\ S_2,\ e_{1,2} = 2 * 2^2 = 2 * 4 = 8 ≠ 6.\)
.
\(\displaystyle For\ S_2,\ e_{2,1} = (2 * 2^2) + 2 = 8 + 2 = 10 ≠ 7.\)
.
\(\displaystyle For\ S_2,\ e_{2,2} = (2 * 2^2) + (2 * 2) = 8 + 4 = 12 ≠ 9.\)
Click to expand...

It's asking for the sum of all the matrices.
 
MathStudent1999 said:
It's asking for the sum of all the matrices.
Click to expand...
What you originally said was asked was the sum of the elements in matrix Sk.
MathStudent1999 said:
What is the sum of the entries in Sk? Express your answer in term of k.
Click to expand...
What you gave did not appear to be a sum of elements but a matrix itself. So I thought you were giving the general formula for matrix k. If in fact the question is asking for the sum of matrix S1 through Sk, then you have found a correct answer.
 
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Hello, MathStudent1999!

\(\displaystyle \text{If }\,S_1 = \begin{bmatrix}1&2\\3&4\end{bmatrix},\;S_2 = \begin{bmatrix}5&6\\7&8\end{bmatrix},\;S_3 = \begin{bmatrix}9&10\\11&12\end{bmatrix},\;S_4 = \begin{bmatrix}13&14\\15&16\end{bmatrix} \)

\(\displaystyle \text{What is the sum of the entries in }S_k?\;\text{ Express your answer in terms of }k.\)

\(\displaystyle \text{I do not know what }\begin{bmatrix}1&2\\3&4\end{bmatrix}\text{ means.}\) . You don't have to know!
Click to expand...

We are given sets of four consecutive numbers.

\(\displaystyle S_1\) has the first four positive integers: \(\displaystyle \{1,2,3,4\}\)
\(\displaystyle S_2\) has the next four integers: \(\displaystyle \{5,6,7,8\}\)
\(\displaystyle S_3\) has the next four integers: \(\displaystyle \{9,10,11,12\}\)
. . And so on.

Can you express the numbers in the \(\displaystyle k^{th}\) set?
Can you find the sum of those numbers?
 
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