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let t : r2 →r2 be the linear transformation that reflects vectors over the y−axis. a) geometrically (that is without computing a

tangare [24]

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

See the figure for the graph:

(a) for any (x, y) ∈ R² the reflection of (x, y) over the y - axis is ( -x, y )

∴ x → -x hence '-1' is the eigen value.

∴ y → y hence '1' is the eigen value.

also, ( 1, 0 ) → -1 ( 1, 0 ) so ( 1, 0 ) is the eigen vector for '-1'.

( 0, 1 ) → 1 ( 0, 1 ) so ( 0, 1 ) is the eigen vector for '1'.

(b) ∵ T(x, y) = (-x, y)

T(x) = -x = (-1)(x) + 0(y)

T(y) = y = 0(x) + 1(y)

Matrix Representation of $T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$

now, eigen value of 'T'

$T - kI = \left[\begin{array}{cc}-1-k&0\\0&1-k\end{array}\right]$

after solving the determinant,

we get two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Hence,

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Learn more about " Matrix and Eigen Values, Vector " from here: brainly.com/question/13050052

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6 0

1 year ago

Assume that women's heights are normally distributed with a mean given by mu equals 62.5 in, and a standard deviation given by

kirza4 [7]

Answer: a) The probability is approximately = 0.5793

b) The probability is approximately=0.8810

Step-by-step explanation:

Given : Mean : $\mu= 62.5\text{ in}$

Standard deviation : $\sigma = \text{2.5 in}$

a) The formula for z -score :

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Sample size = 1

For x= 63 in. ,

$z=\dfrac{63-62.5}{\dfrac{2.5}{\sqrt{1}}}=0.2$

The p-value = $P(z$

$0.5792597\approx0.5793$

Thus, the probability is approximately = 0.5793

b) Sample size = 35

For x= 63 ,

$z=\dfrac{63-62.5}{\dfrac{2.5}{\sqrt{35}}}\approx1.18$

The p-value = $P(z$

$= 0.8809999\approx0.8810$

Thus , the probability is approximately=0.8810.

6 0

3 years ago

Samantha is making soup. to make the broth, she combines 2/5 cup of vegetable stock and 2/3 cup of chicken soup stock. Boiling

storchak [24]

First,you do,2/5+2/3,but since you will need a common denominator,you will find the least common denominator for 5 and 3.The LCD(Least Common Denominator) will be 15 since both 5 and 3 could go in 15.Now,the equation looks like this: 2/15+2/15 since whatever you do to the bottom numbers,you NEED to do to the top numbers:2 and 2.Now you will need to do,2x3,since 5x3=15 and the answer to 2x3=6 then you do 2x5,since 3x5=15 the answer is 10 now the equation looks like this:6/15+10/15 now you add them together,and the answer will be 16/15 and if you want the answer to be a mixed number,it would look like this: 1 1/15. Hope this helps!

6 0

3 years ago

Read 2 more answers

Question set 2: Many species of terrestrial tree frogs that hibernate at or near the ground surface can survive prolonged exposu

joja [24]

Answer:

0.86

Step-by-step explanation:

The z-score we need to make the comparison is given by

$\bf z=\frac{-2.05-(-2)}{\sigma/\sqrt{n}}$