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Rufina [12.5K]
3 years ago
15

Solve the system by using a matrix equation 7x-4y=4 10x-6y=2

Mathematics
1 answer:
Andrei [34K]3 years ago
3 0

Answer:

<h2>The solution to the system of equation is x = 8, y = 13</h2>

Step-by-step explanation:

The system of equation using matrix equation can be solved using crammers rule. Given the equation;

7x-4y=4

10x-6y=2

The equation will be rewritten in the format AX = B

matrix A will be 2*2 matrix

X will be a column matrix containing the variables

B will be a column matrix

\left[\begin{array}{cc}7&-4\\10&-6\\\end{array}\right] \left[\begin{array}{c}x&y\\\\\end{array}\right] = \right] \left[\begin{array}{c}4&2\\\\\end{array}\right]

first we will find the determinant of the matrix A

|A|=7(-6)-(10)(-4)\\|A|= -42+40\\|A|= -2

To get the value of x, we will substitute the column matrix at the right hand side to replace the first column pf matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.

|X|=\left[\begin{array}{cc}4&-4\\2&-6\\\end{array}\right]\\|X|= -24+8\\|X|=-16

x = |X|/|A|

x = -16/-2

x = 8

Similarly for y, we will substitute the column matrix at the right hand side to replace the second column of matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.

|Y|=\left[\begin{array}{cc}7&4\\10&2\\\end{array}\right]\\|Y|= 14-40\\|Y|=-26

y = |Y|/|A|

y = -26/-2

y = 13

The solution to the system of equation is x = 8, y = 13

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The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population o
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The value of mean, standard deviation and interval from the method of tree ring dating is 1273 AD, 37 years, [1250,1296].

According to the statement

we have to find that the standard deviation, mean and the intervals from the given data.

So, According to the given data from the method of tree ring dating

The value of mean is

x-bar = (1271 + 1208 + 1229 + 1299 + 1268 + 1316 + 1275 + 1317 + 1275) / 9 = x-bar = 1273 AD

And now we find standard deviation :

s = √∑(xi - x-bar) / (N - 1)

∑(xi - x-bar)^2 = (1271 - 1273)2 + (1208 - 1273)2 + (1229 - 1273)2 + ... + (1275 - 1273)2

∑(xi - x-bar)^2 = (-2)2 + (-65)2 + (-44)2 + ... + (2)2

∑(xi - x-bar)^2 = 4 + 4225 + 1936 + 676 + 25 + 1849 + 4 1936 + 4

∑(xi - x-bar)^2 = 10,659

Now,

s^2 = 10659/8 = 1332

s = 37 years

So, standard deviation is 37 years.

We need the t-distribution table since the standard deviation is unknown.  Therefore, our degrees of freedom is 9 - 1 = 8 and the critical value is 1.860.  Set up the confidence interval for the mean:

[x-bar ± t*(s/√n)] = [1273 ± 1.860*(37/√9)]

[x-bar ± t*(s/√n)] = [1250,1296]

So, The value of mean, standard deviation and interval from the method of tree ring dating is 1273 AD, 37 years, [1250,1296].

Learn more about method of tree ring dating here

brainly.com/question/15107034

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

For more data please see the image below.

#SPJ4

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