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pishuonlain [190]
2 years ago
11

How to do matrix multiplication to find unknown matrix?

Mathematics
1 answer:
RoseWind [281]2 years ago
8 0
This is quite difficult to try to explain so I'm going to set up some matrices to demonstrate as best as I can.  If matrix A has 3 rows and 2 columns, it would be respresented as A_{3*2}.  This matrix can only be multiplied by another matrix that has the same number off rows as the number of columns in A.  For example, if matrix B has 2 rows and 3 columns, it would be represented as B_{2*3}. If we set them next to each other, it might be easier to see the rule: A_{3*2} B_{2*3}.  The 2's match, and the other numbers represent how your solution matrix will look.  Your solution matrix will be a 3x3.  Here is matrix A: \left[\begin{array}{ccc}1&2\\3&4\\5&6\end{array}\right] and here's B: \left[\begin{array}{ccc}1&2&3\\4&5&6\\\end{array}\right].  We can multiply these according to the rules.  The multiplication works like this: \left[\begin{array}{ccc}1&2\\3&4\\5&6\end{array}\right] *  \left[\begin{array}{ccc}1&2&3\\4&5&6\\\end{array}\right].  first row of A times first column of B: (1*1)+(2*4) = 9.  that goes into row 1 column 1 of your solution matrix.  Go va to row 1 in A but column 2 in B: (1*2)+(2*5) = 12.  That goes into row 1 column 2 of your solution matrix.  Next row 1 of A and column 3 of B: (1*3)+(2*6) = 15.  That goes into the first row column 3 of the solutiong matrix.  Now move to row 2 of A column 1 of B: (3*1)+(4*4) = 19.  That goes into row 2 column 1 in your solution matrix.  Next row 2 A, column 2 B: (3*2)+(4*5) = 26.  That goes into row 2 column 2 solution matrix. Continue as I showed you.  You should be fine.
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Missing part of the question

Determine the number of handshakes, i, that will occur for each number of people, n, in a particular room. (people)

Answer:

S_n = \frac{n}{2}(n - 1)

Step-by-step explanation:

Given

For 5 people

\begin{array}{cc}{People} & {Handshakes} & {5} & {4} & {4} & {3} & {3} & {2} & {2} & {1} & {1} & {0} &{Total} & {10} \ \end{array}

Using the given instance of 5 people, the number of handshakes can be represented as:

(n - 1) + (n - 2) + (n - 3) + ........ + 3 + 2 + 1 + 0

The above sequence is an arithmetic sequence and the total number of handshakes is the sum of n terms of the sequence.

S_n = \frac{n}{2}{(T_1 + T_n})

Where

T_1 = n - 1 --- The first term

T_n = 0 --- The last term

So:

S_n = \frac{n}{2}(n - 1 + 0)

S_n = \frac{n}{2}(n - 1)

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Answer:

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Step-by-step explanation:

Given

\triangle CAE -- Bigger Triangle

\triangle CBD -- Smaller Triangle

k = \frac{4}{3} --- Scale factor

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Required

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The area of triangle CBD is:

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The area of CAE is:

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Where:

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H = \frac{4}{3}h

The above values is the dimension of the larger triangle (after dilation).

So, we have:

A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h

A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h

A_2 = \frac{1}{2}*\frac{16}{9}  *b* h

Re-order

A_2 = \frac{16}{9}*\frac{1}{2}* b* h

A_2 = \frac{16}{9}*\frac{1}{2}bh

Recall that:

\frac{1}{2}bh = 9

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