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2 years ago

Write the augmented matrix for each system of equations. 9x-4y-5z=9 7x+4y-4z=-1

Mathematics

2 answers:

Masja [62]2 years ago

6 0

Answer:

The augmented matrix is:

$\begin{bmatrix}9 & -4 & -5 & |9\\ 7 & 4 & -4 & |-1\end{bmatrix}$

Step-by-step explanation:

<u>Augmented matrix:</u>

It is a matrix form of a linear system of equations obtained from the coefficient matrix. It is created by adding an additional column of for the constants on the right hand side of the equal sign.

Here we are given a system of linear equations as:

$9x-4y-5z=9$

and $7x+4y-4z=-1$

Hence, the augmented matrix formed is as follows:

$\begin{bmatrix}9 & -4 & -5 & |9\\ 7 & 4 & -4 & |-1\end{bmatrix}$

lakkis [162]2 years ago

4 0

$\left[\begin{array}{ccc|c}9&-4&-5&9\\7&4&-4&-1\end{array}\right]$

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a circular dog pen has a circumference of 78.5 feet. approximate by 3.14 and estimate how many hunting dogs could be safely kept

olasank [31]

Answer:

Step-by-step explanation:

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Art [367]

Answer:

See below

Step-by-step explanation:

3. What are two ways that a vector can be represented?

Considering a vector $\vec{v}$ in some vector space $\mathbb R^n$ we have

$\vec{v} = \langle a,b\rangle$

This is the component form. I don't like that way. It is probably used in high school, but

$\vec{v} = \begin{pmatrix} a\\ b\\ \end{pmatrix}$

is preferable because the inner product on $\mathbb R^n$ is defined to be

$\langle a,b\rangle := \sum_{i = 1}^n a_i b_i$

You can also write it using linear form such as $\vec{v} = 2i+2j$

For this question, I think you meant

vectors

$\vec{u_1} = (-8, 12)$

$\vec{u_2} = (13, 15)$

Once

$\cos(\theta)=\dfrac{\vec{u_1} \cdot\vec{u_2}}{||\vec{u_1}||||\vec{u_2}||}$

Considering that the dot product is

$\vec{u_1}\cdot \vec{u_2} = (-8)\cdot 13 + 12\cdot 15 = -104+180= 76$

and the norm of $\vec{u_1}$ is $||\vec{u_1}|| = \sqrt{(-8)^2 + 12^2} = \sqrt{64 + 144}= \sqrt{208}$

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Thus,

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grigory [225]

Answer:

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Step-by-step explanation:

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