L(A + B) = L(a1 + b1, a2 + b2, a3 + b3) = [a1 + b1, (a2 + b2)2 + (a3 + b3)2, (a3 + b3)2]
= [a1 + b1, a22 + b22 + 2a2b2 + a32 + b32 + 2a3b3, a32 + b32 + 2a3b3]
= [a1, a22 + a32, a32] + [b1, b22 + b32, b32] + [0, 2a2b2, 2a3b3]
= L(A) + L(B) + [0, 2a2b2, 2a3b3] ≠ L(A) + L(B)
therefore L is not a linear transformation since:
L(A+B) ≠ L(A) + L(B)
L: R3 to R3 defined by L([a1 a2 a3]) = [a1 a2^2+a3^2 a3^2]. Prove that this...
T: R3 to R 2 vector function.Is T a linear transformation or not defined by T(a1,a2, a3) = (0, a3 )
: Let a1, a2, a3, . . . be the sequence of integers defined by a1 = 1 and defined for n ≥ 2 by the recurrence relation an = 3an−1 + 1. Using the Principle of Mathematical Induction, prove for all integers n ≥ 1 that an = (3 n − 1) /2 .
10] Q3. (a) Prove the Bonferroni Inequality on three events A1, A2 and A3: P(An Agn A)21-P(A)- P(A2) - P(Aa) (b) Using the results in Q3.(a), and clearly describing the events At, A2 and A3. construct a 100(1-a)% joint confidence intervals for estima- tion of three parameters, denoted by 01,02 and 03, say.
10] Q3. (a) Prove the Bonferroni Inequality on three events A1, A2 and A3: P(An Agn A)21-P(A)- P(A2) - P(Aa) (b) Using the results in Q3.(a), and...
Matrix notation:
A=(a1,a2,a3.....,an) = [a1 a2 a3 a4 .....an] are they equal?
look at the sample picture A should be matrix but it uses ( )
rather than [ ]
Given that A is an n×n matrix with the property AX = 0 for all X " 1 A=(a,,a,, 0 0 Let a.) Let e, =| | | ← ith element Comment
Consider the sequence {an} defined recursively as: a0 = a1 = a2 = 1, an = an−1+an−2+an−3 for any integer n ≥ 3. (a) Find the values of a3, a4, a5, a6. (b) Use strong induction to prove an ≤ 3n−2 for any integer n ≥ 3. Clearly indicate what is the base step and inductive step, and indicate what is the inductive hypothesis in your proof.
(1 point) The cross product of two vectors in R3 is defined by a2b3a3 02 a1 bs |. Find the matrix A of the linear transformation from R3 to R3 given by ri-v Жи Let v-| 9 Answer: A-
please simply. for a1,a2,a3,a4, & a5
Write the first five terms of the sequence defined recursively. Express the terms as simplified fractions when applicable. 9,- -4,a,=2a 1.5 a 1 04 as-
In a closed cylinder A1, A2 and A3 are the bottom, top and side surfaces respectively. The surfaces are maintained at uniform temperature of T1 = 300 [C], T2 = 200 (C) and T3 = 100 (C). If all surfaces are assumed black surfaces, determine the net radiation heat exchange between A1 and other surfaces (namely A2 and A3). D1 =16 [cm], D3 = 16 [cm] and L =20 [cm). A3 42 A1
Let ai, a2 , аз, bị, b2P3 R. Define T : R3 R2 by Prove T is a linear transformation.
Use mathematical induction to show that P(A1∩A2∩...∩An) = P(A1)P(A2|A1)P(A3|A1∩A2)....P(An|A1∩A2∩...∩ An-1) You can assume that you know P(A|B) = P(A|B)P(B)