Question

Find all values z1 and z2 such that (2, −1, 3), (1, 2, 2), and (−4, z1, z2) do not span R3

Answer #1

do not span R^3 if they are not linearly independent .

system will not have unique solution ,

values are

1.
a) Let: z=rcis(t). Enter an argument of -z.
b) Let:z1=4cis(3π/4) and z2=2cis(π/3).
Calculate z1*(/z2) in polar form. Find its modulus and
principle argument. Calculate (z1/z2) in polar form. Find its
modulus and principle argument.
where /z2: the conjugate of z2

Consider a series AC circuit with Z1 = (2 –j1) ? and Z2
= (1 +j5) ? and Vs = 60/0? V. Find the total circuit impedance and
current? Find the voltage drop across Z1 and Z2?

If we have a competitive industrial form that has the production
function q=z1^(1/4)*z2^(a)z3^(1/4)
q is the output, z1 z2 z3 is the production inputs and a is
parameter.
Assume that production input 2 (z2) is fixed in the short
run
1) Find the short run conditional input demand functions for the
firm
2) Find the short run cost function for the firm
3) Find the short run supply function for the firm
4) what happens to the conditional input demand,...

Suppose (Z1, Z2) is a bivariate Gaussian pair of random
variables with Z1 ~ N (0,1), Z2 ~ (0,1) and cov (Z1, Z2) = -0.5.
Find P (Z2 >2 | Z1=-2). The answer is 0.1241. Can you explain
why? Thank you.

Find all values of c ∈ C such that the linear transformation T ∈
L(C^3) given by T(z1,z2,z3)=(z1 +2z2 +2z3, −z2 +cz3, z3) is
diagonalizable. For those values of c, find a basis of C^3 such
that the matrix of T corresponding to that basis is diagonal.

Find all values of c ∈ C such that the linear transformation T ∈
L(C3) given by T(z1, z2, z3) = (z1 + 2z2 + 2z3, −z2 + cz3, z3) is
diagonalizable. For those values of c, find a basis of C3
such that the matrix of T corresponding to that basis is
diagonal.

Two
standard normal variables Z1 and Z2 are independent. Find the
probability density function of the normal random variable X=3Z1 -
Z2

1. Find the total area under the standard normal curve to the
left of z1 and to the right of z2.
z1 = -1.75, z2 = 1.89
a) 1.0224 b) 0.3231 c) 0.6769 d) 0.0695 e) 0.9305
2.Which of the following statements is false?
a) Normal distributions are symmetric, but they do not have to
be bell-shaped.
b) The standard normal distribution is completely defined by its
mean and standard deviation.
c) For any normal distribution, the mean, median, and...

Question A.
Phenylalanine (Phe) has highly negative value of z1-scale and
positive value of z2-scale. Which of the five statements is/are
correct?
a) Phe has negative charge at pH<7 and positive charge at
pH>7 b) Phe is present in very few proteins c) Phe is a
hydrophobic and bulky amino acid d) Phe has a large aromatic side
chain e) Phe is a big and hydrophilic amino acid
B. Z-scale descriptors are also calculated for
artificial (synthetic) amino acids.
Which...

A solid rod of radius w is concentric with the z-axis from z1 to
z2 and bears a uniform volumetric charge density rho. The
field-point is at the origin. Choose the correct replacement for dQ
in the integral:
1. σwds
2. σ2πldl
4. ρ2πldldz
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