Question

Let T(V)=AV be a linear transformation where A=(3 -2 6 -1 15, 4 3 8 10 -14, 2 -3 4 -4 20)

a.) construct a basis of the kernal T

b.) calculate the basis of the range of T

c.) determine the rank and nullity of T

Answer #1

3 | -2 | 6 | -1 | 15 |

4 | 3 | 8 | 10 | -14 |

2 | -3 | 4 | -4 | 20 |

Divide row1 by 3

1 | -2/3 | 2 | -1/3 | 5 |

4 | 3 | 8 | 10 | -14 |

2 | -3 | 4 | -4 | 20 |

Add (-4 * row1) to row2

1 | -2/3 | 2 | -1/3 | 5 |

0 | 17/3 | 0 | 34/3 | -34 |

2 | -3 | 4 | -4 | 20 |

Add (-2 * row1) to row3

1 | -2/3 | 2 | -1/3 | 5 |

0 | 17/3 | 0 | 34/3 | -34 |

0 | -5/3 | 0 | -10/3 | 10 |

Divide row2 by 17/3

1 | -2/3 | 2 | -1/3 | 5 |

0 | 1 | 0 | 2 | -6 |

0 | -5/3 | 0 | -10/3 | 10 |

Add (5/3 * row2) to row3

1 | -2/3 | 2 | -1/3 | 5 |

0 | 1 | 0 | 2 | -6 |

0 | 0 | 0 | 0 | 0 |

Add (2/3 * row2) to row1

1 | 0 | 2 | 1 | 1 |

0 | 1 | 0 | 2 | -6 |

0 | 0 | 0 | 0 | 0 |

Let the linear transformation T: V--->W be such that T (u) =
u2 If a, b are Real. Find T (au + bv) ,
if u = (x, y) v = (z, w) and uv = (xz-yw, xw + yz)
Let the linear transformation T: V---> W be such that T (u)
= T (x, y) = (xy, 0) where u = (x, y), with 2, -3. Then, if u = (
1.0) and v = (0.1). Find the value...

Let T:V-->V be a linear transformation and let T^3(x)=0 for
all x in V. Prove that R(T^2) is a subset of N(T).

10 Linear Transformations. Let V = R2 and W = R3. Define T: V →
W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation
of T using the standard bases in both V and W
11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0)
= (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2).
Compute T(−2, 4, −1).

(a) Let T be any linear transformation from R2 to
R2 and v be any vector in R2 such that T(2v)
= T(3v) = 0. Determine whether the following is true or false, and
explain why: (i) v = 0, (ii) T(v) = 0.
(b) Find the matrix associated to the geometric transformation
on R2 that first reflects over the y-axis and then
contracts in the y-direction by a factor of 1/3 and expands in the
x direction by a...

Let T be a 1-1 linear transformation from a vector space V to a
vector space W. If the vectors u,
v and w are linearly independent
in V, prove that T(u), T(v),
T(w) are linearly independent in W

let T:P2→P4 be a linear transformation defined by
T(a+bx+cx2)=2bx−cx2−cx4.
(a) Find ker(T) and give a basis for ker(T).
(b) Find range(T)range(T) and give a basis for range(T).
(c) By justifying your answer determine whether T is
one-to-one.
(d) By justifying your answer determine whether T is onto.

consider the basis S={v1,v2} for R^2,where v1=(-2,1) and
v2=(1,3),and let T:R^2-R^3 be linear transformation such that
T(v1)=(-1,2,0) And T(v2)=(0,-3,5), find T(2,-3)

Let T be a linear transformation from Rr to
Rs .
Determine whether or not T is one-to-one in each of the following
situations:
1. r > s
2. r < s
3. r = s
A. T is not a one-to-one transformation
B. T is a one-to-one transformation
C. There is not enough information to tell
Explain reason clearly plz

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)

1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 39 minutes ago

asked 44 minutes ago

asked 44 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 51 minutes ago

asked 59 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago