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DENIUS [597]
2 years ago
15

Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Col

umn EndMatrix x plus 2 y equals 8 nbsp 2 x plus 6 y equals 9 What is the inverse​ matrix?
Mathematics
1 answer:
natali 33 [55]2 years ago
4 0

Answer:

\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

A^{-1} = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = \left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]

A^{-1}= \frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right] = \left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]

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Suppose that 15% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in t
hram777 [196]

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a.\mu=15

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c. Choice A- Based on limits above, it is unlikely that we would see x = 45, so it might be possible that the trials are not independent.

Step-by-step explanation:

a.Binomial distribution is defined by the expression

P(X=k)=C_k^n.p^k.(1-p)^{n-k}

Let n be the number of trials,n=100

and p be the probability of success,p=15\%

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\mu=np=100\times0.15=15

b.Limits within which p is approximately 95%

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Use the empirical rule to find the limits. From the rule, approximately 95% of the observations are within to standard deviations from mean.

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Hence, approximately 95% of the observations are within 7.8586 and 22.1414 (areas of infestation).

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