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 the name of the relationship between ∠3 ​ and ∠7?
lara31 [8.8K]

answer is B) Corresponding angles

6 0
2 years ago
Read 2 more answers
Mrs. Johnson measured 3 rectangular rooms that she wants to tile. What is the total area of the​ rooms?
stich3 [128]

Answer:

Find the area of each room and add the areas

Step-by-step explanation:

Please find the full question in the attached image

the area of rectangle is length x breadth. The area of each room would be found and the three areas would be added together

for example ,

dimension of room 1 = 5 x 3

dimension of room 2 = 2 x 3

dimension of room 3 = 4 x 5

area of room 1 = 15

area of room 2 = 6

area of room 3 = 20

total area = 15 + 6 + 20 = 41

6 0
3 years ago
Solve the given system of equations.<br><br><br> The solution to the system is ( , ).
MAXImum [283]

Answer:

x=3

y=1

Step-by-step explanation:

First, get x and y on the left in the lower equation. -2x+10y=4. Then solve using a calculator. Select (apps), PlySmlt2, Simultaneous EQN Solver, and enter your euqations in.

3 0
2 years ago
Read 2 more answers
30 POINTS!!! NEED HELP!!!!
Kaylis [27]

Answer:

b) 16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121

Step-by-step explanation:

\Sigma_{k=1}^{16} (k - 5)^2 \\= (1- 5)^2 +  (2- 5)^2 +  (3- 5)^2 + \\ (4- 5)^2 +  (5- 5)^2 +  (6- 5)^2 \\+  (7- 5)^2 +  (8- 5)^2 +  (9- 5)^2 \\+  (10- 5)^2 +  (11- 5)^2 +  (12- 5)^2 \\+  (13- 5)^2 +  (14- 5)^2 +  (15- 5)^2\\ +  (16- 5)^2 \\\\=(-4)^2 +  (-3)^2 +  (-2)^2 +  (-1)^2 +  (0)^2 \\+  (1)^2 +  (2)^2 +  (3)^2 +  (4)^2 +  (5)^2 \\+  (6)^2 +  (7)^2 +  (8)^2 +  (9)^2 +  (10)^2 + \\ (11)^2 \\\\=16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 \\+ 36 + 49+ 64 + 81 + 100 + 121

6 0
3 years ago
Solve for f. show your work! 12=f-13-2
tankabanditka [31]
12=f-13-2
12=f-15
f=27
3 0
3 years ago
Read 2 more answers
Other questions:
  • A triangle has a height that is 2 inches more than three times the base and an area of 60 in. Find the base and the height of th
    10·1 answer
  • A real estate developer builds a small number of model homes, one each in a different style. During an open house event, there i
    13·1 answer
  • Explain why the absolute value of a number is never negative
    12·1 answer
  • -g + 2(3 + g) = -419 + 1)<br> What is the solution
    7·2 answers
  • How many meters is 7.3 kilometers? 1km=1000m
    8·2 answers
  • The table below show the amount of water that is in a bathtub that is being filled
    5·1 answer
  • If 4x = 28, find the value of 29 - 5x
    5·2 answers
  • The formula for the area of a triangle is A = = { bh. Find the area of a triangle with a base (b) of 7 feet and a height (h) of
    15·1 answer
  • What happens to a graph that is representative of exponential decay? The graph goes:
    15·1 answer
  • What is 1 1/2 multiply 12
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!