If the matrix A is 4×2, B is 3×4, C is 2×4, D is 4×3,
and...
If the matrix A is 4×2, B is 3×4, C is 2×4, D is 4×3,
and E is 2×5, what are the
dimensions of the following expressions
a) A^TD + CB^T
b) (B + D^T ) A
c) CA + CB^T
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an
example of a function f: A -> A with the indicated properties,
or explain why no such function exists.
(a) f is bijective, but is not the identity function f(x) =
x.
(b) f is neither one-to-one nor onto.
(c) f is one-to-one, but not onto.
(d) f is onto, but not one-to-one.
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. 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?
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8,...
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8, 10, 12}, and C
= {4, 5, 6, 7, 8, 9, 10}.
Determine the following sets:
i. (A ∩ B) − C
ii. (A − B) ⋃ (B − C)
4. Let A = {1, 2, 3, 4, 5}. Let L = {(x, y) ∈ A...
4. Let A = {1, 2, 3, 4, 5}. Let L = {(x, y) ∈ A × A : x < y}
and B = {(x, y) ∈ A × A : |x − y| = 1}.
i. Draw graphs representing L and B.
ii. Determine L ◦ B.
iii. Determine B ◦ B.
iv. Is B transitive? Explain.
1. In creating a Dimension Style named WALLSEC3_4, if the
feature size you enter for text...
1. In creating a Dimension Style named WALLSEC3_4, if the
feature size you enter for text height is 1/8", the absolute text
height in Model Space will be _______. A. 1/2" B. 1 1/2" C. 2" D.
6" E. 12"
2. Which of the following would be the correct Dimension Feature
Scale Factor for a Dimension Style named DOORDTLS3? A. 48 B. 32 C.
24 D. 12 E. 4
3. Which of the following would be the correct Dimension Feature...
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases...
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases
for R2, and
let A =
3
2
0
4
be the matrix for T: R2 ? R2 relative to B.
(a) Find the transition matrix P from B' to B. P =
(b) Use the matrices P and A to find [v]B and [T(v)]B, where
[v]B' = [1 ?5]T. [v]B = [T(v)]B =
(c) Find P?1 and A' (the matrix for T relative...
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be...
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be three points
in R^3
a) give the parametric equation of the line orthogonal to the
plane containing A, B and C and passing through point A.
b) find the area of the triangle ABC
linear-algebra question
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2. Let P 1 and P2 be planes with general equations P1 : −2x + y...
2. Let P 1 and P2 be planes with general equations P1 : −2x + y
− 4z = 2, P2 : x + 2y = 7.
(a) Let P3 be a plane which is orthogonal to both P1 and P2. If
such a plane P3 exists, give a possible general equation for it.
Otherwise, explain why it is not possible to find such a plane. (b)
Let ` be a line which is orthogonal to both P1 and P2....