1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Musya8 [376]
3 years ago
6

Assume that T is a linear transformation. Find the standard matrix of T. T: R^3 right arrow R^2 , T(e 1) =(1,2), and T(e2 ) =( -

4,6), and T(e 3 ) =(2, -6), where e 1, e2 , and e 3 are the columns of the 3 x 3 identity matrix. A= (Type an integer or decimal for each matrix element.)
Mathematics
1 answer:
irina [24]3 years ago
6 0

Answer:

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

Step-by-step explanation:

Given

T:R^3->R^2

T(e_1) = (1,2)

T(e_2) = (-4,6)

T(e_3) = (2,-6)

Required

Find the standard matrix

The standard matrix (A) is given by

Ax = T(x)

Where

T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]

Ax = T(x) becomes

Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]

The x on both sides cancel out; and, we're left with:

A = [T(e_1)\ T(e_2)\ T(e_3)]

Recall that:

T(e_1) = (1,2)

T(e_2) = (-4,6)

T(e_3) = (2,-6)

In matrix:

(a,b) is represented as: \left[\begin{array}{c}a\\b\end{array}\right]

So:

T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]

T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]

T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]

Substitute the above expressions in A = [T(e_1)\ T(e_2)\ T(e_3)]

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

Hence, the standard of the matrix A is:

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

You might be interested in
What is 16,473 to the nearest hundred
Verizon [17]
The number "4" is in the hundreds place. To the right is 7, and since it's greater than five it rounds up. So 16,473 to the nearest hundred is 16,500. Hope this helped!
4 0
3 years ago
Lily wants to buy a smartphone, she has $500 to spend .list three ways she can get a good deal
BaLLatris [955]
1. Check the prices of phones from different stores.

2. Do some research to see what is the average cost of the phone.

3. Check for possible discounts.

Hope this helps :)

3 0
3 years ago
21.79 + x = 25<br><br><br> make sure to do a explanation
laiz [17]

Answer:

x= 3.21

Step-by-step explanation:

25- 21.79= 3.21

the equation equals to 25 so you need to find what x is by subtracting the other value

Hope this helps

6 0
2 years ago
Today only, a desk is being sold at a 33% discount. The sale price is $268. What was the price yesterday?
Serga [27]

Discount percent = 33%

Sale price = $268

Let the original price be $x.

So,

x - (33\% \: of \: x) = 268 \\  =  > x - ( \frac{33}{100}  \times x) = 268 \\  =  > x - ( \frac{33x}{100}) = 268 \\  =  >  \frac{100x}{100}  -  \frac{33x}{100}  = 268 \\  =  >  \frac{(100x - 33x)}{100}  = 268 \\  =  >  \frac{67x}{100}  = 268 \\  =  > 67x = 268 \times 100 \\  =  > 67x = 26800 \\  =  > x =  \frac{26800}{67}  \\  =  > x = 400

So, yesterday the price was $400.

5 0
3 years ago
Rewrite this formula to convert Fahrenheit to Celsius. F= 9/5C + 35
iVinArrow [24]

Answer:

\huge \purple { \boxed{ C = \frac{5}{9} ( F  - 32)}}

Step-by-step explanation:

I the given problem, there should be 32 in place of 35.

F =  \frac{9}{5}  C + 32 \\ F  - 32=  \frac{9}{5}  C \\ 5( F  - 32)=  9  C \\  \frac{5}{9} ( F  - 32)=C \\  \\ \huge \red{ \boxed{ C = \frac{5}{9} ( F  - 32)}}

7 0
3 years ago
Other questions:
  • Right away to compare 200 meters to 4 hours
    8·1 answer
  • Simplify the following expression. a^-3/a^-3
    7·1 answer
  • The number of chocolate chips in a popular brand of cookie is normally distributed with a mean of 22 chocolate chips per cookie
    15·2 answers
  • clayton open a savings account 4 years ago. the account earns 8% interest, compounded monthly. if the current balance is $200.00
    9·1 answer
  • I am trying to keep up with math so can you help me
    11·1 answer
  • 1. Explain why 3(x + 4) = 3(x - 5) has no solution.
    5·1 answer
  • Twain's decision to end "The War Prayer" with the townspeople ignoring what
    8·1 answer
  • Need this done by today! 2-2-2021
    10·2 answers
  • Please answer this question step by step!
    6·1 answer
  • Domain of<br> What is the<br> the function y-x?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!