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Alexandra [31]
2 years ago
11

Construct an augmented matrix for this linear system: x − y − 4z = 5 2x 2z = 0 4x y z = 3.

Mathematics
2 answers:
Leviafan [203]2 years ago
8 0

The augmented matrix for the given linear equations will be constructed as follows

\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]

<h3>What will be the augmented matrix of the given linear equations?</h3>

The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.

The given equation has three variables so the matrix form will be of 3\times3

The given linear equations are

x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3

From the above equations, we will make an augmented matrix.

\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]

The first equation will be followed by the first row of the matrix and the rest will be followed the same.

Thus the augmented matrix for the given linear equations will be constructed as follows

\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]

To learn more about the Augmented matrix follow

brainly.com/question/26103226

Crazy boy [7]2 years ago
7 0

The augmented matrix is,

\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)

We have given system of linear equation is,

x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.

<h3>What is the meaning of augmented matrix?</h3>

In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.

So, the first row is

1\ -1\ -4\ 5

the second row is

2\ 0\ 2\ 0

and the third row is

4\ 1\ 1\ 3

Therefore the augmented matrix for this linear system is,

\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)

To learn more about the augmented matrix visit:

brainly.com/question/14600951

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Answer:

Hotdog: $3.00

Hamburger: $4.00

Step-by-step explanation:

For the first time that Bob buys food, we can make an equation to find how much a single hotdog and a single hamburger costs, where:

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y = cost of a hamburger

He bought 2 hotdogs and 1 hamburger for $10, so the equation for his first time buying food is:

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For the second time buying food, he bought 1 hotdog and 3 hamburgers for $15, so his equation would be:

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To find the value for x and y we need to solve this system of equations using the two equations we just came up with. We can do this multiple ways, but I'll be demonstrating the substitution method.

Using the second equation, we can solve for x by simply subtracting 3y from both sides:

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We can then insert this value of x into the first equation so that way we are only dealing with one variable to solve - y:

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This means the cost for one hamburger is $4. But we still need to find the price of one hotdog, so we can insert this value of y into the equation we came up with earlier for x, and then solve for x:

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Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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