Here is 3 & 4 I NEED DONE ASAP!

Given matrices are from here

link

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Problem 3

a)

B - C = DNE

We cannot subtract matrices of different sizes. Matrix B is 2x2 while C is 3x2. Both matrices must have the same number of rows, and they must also have the same number of columns. The matrices don't have to be square.

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b)

You add the corresponding elements. For instance, in the top left corner we have -1+(-4) = -5. The other entries are treated in a similar manner.

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c)

You get this from multiplying each entry in matrix E by -2. Eg: top left corner has -2*(-3) = 6

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d)

Matrix C has 3 rows and D has 3 columns. The final answer will be size 3x3

To generate each value in the answer matrix, you'll highlight rows of C to pair with columns of D. Then you'll multiply out the corresponding values, after which you add those products. This is done for every entry in the answer shown above.

For example, the first row of C is highlighted and the second column of D is highlighted. Those values pair up and multiply getting -1*(-1) + 2*3 = 1+6 = 7, which goes in the first row and second column of the answer matrix. The other entries are handled in a similar fashion.

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e)

The 2x2 matrix determinant formula is

In this case, a = -4, b = 6, c = 5, d = 4.

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f)

Swap the top left and bottom right corners of matrix B. Change the sign of the other two corner values. Then multiply each entry by 1/d where d is the determinant found back in part (e) above. Be sure to reduce any fraction as much as possible.

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Problem 4

Answers: x = 2  and y = -10

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Work Shown:

In the top left corners of each matrix, in line 3, we have 2x+3 = 7 which solves to...

2x+3 = 7

2x = 7-3

2x = 4

x = 4/2

x = 2

In the bottom right corners, we have y-3 = -13 which solves to....

y-3 = -13

y = -13+3

y = -10

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

The sample 2, of size n2=150 has a proportion of p2=0.7333.

The difference between proportions is (p1-p2)=0.1167.

The pooled proportion, needed to calculate the standard error, is:

The estimated standard error of the difference between means is computed using the formula:

Then, we can calculate the z-statistic as:

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.