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Natasha2012 [34]
3 years ago
8

Which equation can be used to solve the matrix equation?

Mathematics
2 answers:
qwelly [4]3 years ago
5 0

Answer:

The correct option is 4.

Step-by-step explanation:

The given matrix equation is

\begin{bmatrix}\frac{1}{2} & \frac{-1}{4}\\ 2 & -\frac{3}{4}\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}2 & -4\\ 1 & 6\end{bmatrix}

Let A=\begin{bmatrix}\frac{1}{2} & \frac{-1}{4}\\ 2 & -\frac{3}{4}\end{bmatrix}, X=\begin{bmatrix}x\\ y\end{bmatrix} and B=\begin{bmatrix}2 & -4\\ 1 & 6\end{bmatrix}

The given equation can be written as

AX=B

If AX=B, then X=A^{-1}B

It means we have to find the matrix A⁻¹ .

A=\begin{bmatrix}\frac{1}{2} & \frac{-1}{4}\\ 2 & -\frac{3}{4}\end{bmatrix}

|A|=\frac{1}{2}\times \frac{-3}{4}-\frac{-1}{4}\times 2=\frac{-3}[8}+\frac{1}{2}=\frac{1}{8}

If P=\begin{bmatrix}a & b\\ c & d\end{bmatrix}, then P^{-1}=\frac{1}{|P|}\begin{bmatrix}d &-b\\ -c & a\end{bmatrix}

A^{-1}=\frac{1}{\frac{1}{8}}\begin{bmatrix}-\frac{3}{4}& \frac{1}{4}\\ -2 &\frac{1}{2}\end{bmatrix}

A^{-1}=8\begin{bmatrix}-\frac{3}{4}& \frac{1}{4}\\ -2 &\frac{1}{2}\end{bmatrix}

A^{-1}=\begin{bmatrix}-6& 2\\ -16 &4\end{bmatrix}

X=A^{-1}B

\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}-6& 2\\ -16 &4\end{bmatrix}\begin{bmatrix}2 & -4\\ 1 & 6\end{bmatrix}

Therefore the correct option is 4.

Tasya [4]3 years ago
4 0

Answer:

A matrix equation is an equation in which a variable stands for a matrix . You can solve the simpler matrix equations using matrix addition and scalar multiplication .

Step-by-step explanation:

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Step-by-step explanation:

hope it helps .

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The number of hours a group of 12 children in Mrs. Smith's kindergarten class read in a day.
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The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past
galina1969 [7]

Complete Question

The complete question is shown on the uploaded image  

Answer:

1 ) The correct option B

2) The correct option is  C

3)  The correct option is  C

4)  The correct option is  C

Step-by-step explanation:

From the question we are told that

   The proportion that own a cell phone  is  p = 0.90

    The  sample  size is  n =  15

Generally the appropriate distribution for X is mathematically  represented as

      X  \ is  \ B( n , p )

So  

       X  \ is  \ B( 15 , 0.90 )

Generally the number students that  own a cell phone in a simple random sample of 15 students is mathematically represented as

              \mu  =  n  *  p

              \mu  =  15 *  0.90

              \mu  =   13.5

Generally the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is mathematically represented as

                \sigma  =  \sqrt{ n *  p *  q }

Where  q is mathematically evaluated as

          q =  1- p

           q =  1- 0.90

           q =  0.10

            \sigma  =  \sqrt{ 15 *  0.90 *  0.10 }

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Generally the probability that all students in a simple random sample of 15 students own a cell phone is mathematically represented as

   P(X =  15) =  \left 15} \atop {}} \right.C_{15} *  p^{15} *  q^{15 - 15}    

     P(X =  15) =  \left 15} \atop {}} \right.C_{15} *  (0.90)^{15} *  (0.10 )^{15 - 15}

From the combination calculator  is      \left 15} \atop {}} \right.C_{15} =  1

     P(X =  15) = 1 *  0.205891 *  1

      P(X =  15) = 0.206

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Taken together, we find that (0, 0, 0) appears to be the only critical point on f within the ball. At this point, we have f(0,0,0)=0.

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L_x=5yz+2\lambda x=0
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3 years ago
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