Question

Consider the matrix transformation

T(x,y,z) = (-x+y+z, 2x-y, 18x+y+ 18z)

from R^{3} to R^{3}

Then the sum of the elements of the last row of the standard matrix
of T is

Answer #1

If any doubt please comment.

Consider the transformation T: R2 -> R3 defined by
T(x,y) = (x-y,x+y,x+2y)
Answer the Following
a)Find the Standard Matrix A for the linear transformation
b)Find T([1
-2])
c) determine if c = [0 is in the range of the transformation
T
2
3]
Please explain as much as possible this is a test question that
I got no points on. Now studying for the final and trying to
understand past test questions.

b) More generally, find the matrix of the linear transformation
T : R3 → R3 which is u1
orthogonal projection onto the line spanu2. Find the matrix of T.
Prove that u3
T ◦ T = T and prove that T is not invertible.

let let T : R^3 --> R^2 be a linear transformation defined by
T ( x, y , z) = ( x-2y -z , 2x + 4y - 2z) a give an example of two
elements in K ev( T ) and show that these sum i also an element of
K er( T)

Consider the system of linear equations 2x+y-3z=-7 x+y-z=-1
4x+3y-5z=-9 (a)Represent this system as a matrix A (b)Use row
operations to transform A into row echelon form Use your answer to
(b) to find all non-integer solutions of the system

Let T be the function from R2 to R3 defined by T ( (x,y) ) = (x,
y, 0). Prove that T is a linear transformation, that it is 1-1, but
that it is not onto.

Consider the linear transformation P : R3 → R3 given by
orthogonal projection onto the plane 3x − y − 2z = 0, using the dot
product on R3 as inner product.
Describe the eigenspaces and
eigenvalues of P, giving specific
reasons for your answers. (Hint: you do not need
to find a matrix representing the transformation.)

Find a basis B for the domain of T such that the matrix for T
relative to B is diagonal.
T: R3 → R3: T(x, y, z) = (−4x + 2y − 3z, 2x − y − 6z, −x − 2y −
2z)
B =

Find a basis B for the domain of T such that the matrix for T
relative to B is diagonal. T: R3 → R3: T(x, y, z) = (−5x + 2y − 3z,
2x − 2y − 6z, −x − 2y − 3z)

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as
T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z)
Find the standard matrix for T and decide whether the map T is
invertible.
If yes then find the inverse transformation, if no, then explain
why.
b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x...

Find a basis B for the domain of T such that the matrix for T
relative to B is diagonal. T: R3 → R3: T(x, y, z) = (−5x + 2y − 3z,
2x − 2y − 6z, −x − 2y − 3z) B = Incorrect: Your answer is
incorrect.

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