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
Alja [10]
3 years ago
6

Determine if the specified linear transformation is ​(a​) ​one-to-one and ​(b​) onto. Justify your answer. ​T: ​, ​T(​)​(​,​), ​

T(​)​(​,​), and ​T(​)​(​,​), where ​, ​, are the columns of the 33 identity matrix. a. Is the linear transformation​ one-to-one? A. T is​ one-to-one because ​T(x​)0 has only the trivial solution. B. T is not​ one-to-one because the columns of the standard matrix A are linearly independent. C. T is not​ one-to-one because the standard matrix A has a free variable. D. T is​ one-to-one because the column vectors are not scalar multiples of each other. b. Is the linear transformation​ onto? A. T is onto because the columns of the standard matrix A span . B. T is not onto because the columns of the standard matrix A span . C. T is onto because the standard matrix A does not have a pivot position for every row. D. T is not onto because the standard matrix A contains a row of zeros.
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
8 0

Answer:

C. T is not​ one-to-one because the standard matrix A has a free variable.

Step-by-step explanation:

Given

T(x_1,x_2,x_3) = (x_1-5x_2+4x_3,x_2 - 6x_3)

Required

Determine if it is linear or onto

Represent the above as a matrix.

T(x_1,x_2,x_3) = \left[\begin{array}{ccc}1&-5&4\\0&1&-6\\0&0&0\end{array}\right]  \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right]

From the above matrix, we observe that the matrix does not have a pivot in every column.

This means that the column are not linearly independent, & it has a free variable and as such T is not one-on-one

You might be interested in
What is the greatest fraction you can make using the digits 4, 7, and 9?
wel

Answer:

  (7^9)/4 = 40,353,607/4

Step-by-step explanation:

Assuming each digit is used once and exponentiation is allowed, the largest numerator and smallest denominator will result in the largest fraction.

__

If other functions, such as factorial are allowed, then there might need to be a limit on the number of times they are applied. For example,

  (7!)^(9!)/4 has about 1 million digits

something like ...

  ((7!)^(9!))!/4 has many more digits than that

and you can keep piling on the factorial symbols to any desired depth.

6 0
3 years ago
Given two angles that measure 50 degrees and 90 degrees and a side that measures 4 feet​
kupik [55]

What is the question? Please specific!

7 0
3 years ago
Read 2 more answers
What is the 100th term in the following sequence: 25, 36, 49, 64...
Mandarinka [93]
The sequence is given by (n+5)²
For n=100:
(100+5)² = 105² = 11025
7 0
3 years ago
Please help with A.
Furkat [3]

Answer:

ok so I dont have the answer but I suggest if u can u do the tutor they help a lot u can only ask 1 question per session but trust me it's helpful

they also say the answer at the end

so first they explain how to get the answer like they do the math

3 0
3 years ago
You are at a sandwich shop. You can choose from white or rye bread, turkey or ham, and Swiss or American
Gre4nikov [31]

Answer: The correct is answer is: The subset consists of all the sandwiches with either white bread and ham or rye bread and turkey.

Step-by-step explanation: I got this question correct.

6 0
3 years ago
Other questions:
  • Solve the problem as directed.
    6·1 answer
  • A new computer system sells for approximately $2000 and depreciates at the rate of $500 per year.
    6·1 answer
  • I need help on this pls
    7·1 answer
  • how many different four letter permutations can be formed using four letters out of the first 12 in the alphabet?
    14·1 answer
  • WILL GIVE BRAINLIEST AND 30 POINTS!
    15·2 answers
  • HELP ASAP PLEASE!
    13·1 answer
  • Jake created a scale drawing of an airplane. In the scale drawing, the length of the airplane was 15 inches. The length of the a
    12·1 answer
  • 1.682 inches rounded to the nearest whole number is 1 inches?
    7·2 answers
  • What is the rate of change of the graph shown below?<br><br> PLS HELP!!!! ^^^
    12·1 answer
  • I will give brainliest to the first person to answer
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!