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3 years ago

A geometric transformation that does not change the shape or size of the geometric object is called a

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

8 0

Answer:

Univ.

Explanation:

A geometry transformation is either rigid or non-rigid; another word for a rigid transformation is "isometry". An isometry, such as a rotation, translation, or reflection, does not change the size or shape of the figure.

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Consider the following two ordered bases of R3:

grigory [225]

Answer:

Let $A = (a_1, ..., a_n)$ and $B = (b_1, ..., b_n)$ bases of V. The matrix of change from A to B is the matrix n×n whose columns are vectors columns of the coordinates of vectors $b_1, ..., b_n$ at base A.

The, we case correspond to find the coordinates of vectors of C,

$\{\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right], \left[\begin{array}{ccc}2\\0\\-1\end{array}\right], \left[\begin{array}{ccc}-3\\1\\2\end{array}\right] \}$

at base B.

1. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&2\\-1&2&-1&-1\\0&-1&1&-1\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&2\\0&-1&1&-1\\0&0&1&1\end{array}\right]$

now we use backward substitution

$c=1\\-b+c=-1,\; b=2\\a-2b+2c=2,\; a=4$

Then the coordinate vector of $\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right]$ is $\left[\begin{array}{ccc}4\\2\\1\end{array}\right]$

2. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}2\\0\\-1\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&2\\-1&2&-1&0\\0&-1&1&-1\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&2\\0&-1&1&-1\\0&0&1&2\end{array}\right]$

now we use backward substitution $c=2\\-b+c=-1,\; b=3\\a-2b+2c=2,\; a=4$

Then the coordinate vector of $\left[\begin{array}{ccc}2\\0\\-1\end{array}\right]$ is $\left[\begin{array}{ccc}4\\3\\2\end{array}\right]$

3. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}-3\\1\\2\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&-3\\-1&2&-1&1\\0&-1&1&2\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&-3\\0&-1&1&2\\0&0&1&-2\end{array}\right]$

now we use backward substitution $c=-2\\-b+c=2,\; b=-4\\a-2b+2c=2,\; a=-2$

Then the coordinate vector of $\left[\begin{array}{ccc}-3\\1\\2\end{array}\right]$ is $\left[\begin{array}{ccc}-2\\-4\\-2\end{array}\right]$

Then the change of basis matrix from B to C is

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

4 0

4 years ago

Please solve with explanation 20 points

Vinil7 [7]

Answer:

a its parallel

b its parallel

c its parallel

Step-by-step explanation:

i dont know it's about parallel

6 0

3 years ago

What's the value of<br> z? - 3x + 1<br> when x = -2 and y = 42

sveticcg [70]

Answer: 11

Step-by-step explanation:

Based on te question in the picture (which is different from what you wrote)

x^2 - 3x + 1

-2^2 - 3(-2) + 1

4 + 6 + 1 = 11

3 0

3 years ago

Write an equation for the line that passes through the points (0,-6) and (-3,0)

lisov135 [29]

Answer:

Then the desired equation is y = -2x - 6.

Step-by-step explanation:

As we move from point (-3, 0) to point (0, -6), x increases by 3 and y decreases by 6. Thus, the slope of the line segment connecting these two points is m = rise / run = -6/3 = -2.

Now use the slope-intercept equation of a straight line to determine the y-intercept of this line:

y = mx + b becomes 0 = -2(-3) + b, so that b = -6.

Then the desired equation is y = -2x - 6.

Check: Does (0, -6) satisfy y = -2x - 6? Is -6 = -2(0) - 6 true? YES

7 0

3 years ago

There are seven black socks, eight blue socks, 10 white socks, and five patterned socks in the drawer. What is the probability o

Jet001 [13]

Answer:

2/45

Step-by-step explanation:

Total socks:

7 + 8 + 10 + 5 = 30

P(blue) × P(patterned)

8/30 × 5/30

4/15 × 1/6

2/45

4 0

3 years ago

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