Question

Suppose a 3x3 real matrix A=[a b c; d e f; g h i] has determinant 5. What is the determinant of the 3x3 matrix B=[2a 2c 2b; 2d 2f 2e; 2g 2i 2h]?

Answer #1

Using this matrix.
A =
a
b
c
d
e
f
g
h
i
Suppose that det(A) = 5. Find the determinant of the
following matrix.
B =
a + 3g
b + 3h
c + 3i
-g
-h
-i
4d
4e
4f

9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a partition of S?
Explain.
b. is {{a, b}, {c, d}, {e, f}, {g, h}, {h, i, j}} a partition
of S? Explain. c. is {{a, b}, {c, d}, {e, f}, {g, h}, {i, j}} a
partition of S? Explain.

Given that, for some a, b, c, d, e, f, g, h, i ∈ R, [a b c d e f
g h i ] = 5, evaluate the following determinants:
(c) [ka ld mg
kb le mh
kc lf mi] Here, k, l, and m are non-negative constants.

1) The enthalpy change (∆H) of each of the two reactions is
given as follows:
A + B = 1/2C + 1/2D ∆H = - 30 J/mol
C + D = 2E + 2F ∆H = 80 J/mol
What is the enthalpy change (∆H) of the following reaction?
A + B = E + F ∆H = ? J/mol
2) The enthalpy change (∆H) of each of the two reactions is
given as follows:
A + B = C +...

Suppose that f(x) = x^2, g(x) = sin(x) and h(x) = e^x. Using the
appropriate rules, find the derivatives of the following
functions:
A. 3f−2g
B. fg
C. fh
D. f◦g
E. g◦f

Find the number of permutations of a, b, c, d, e, f, g and h
containing no piece ab, or cd, or acb.

How many permutations of the set {A, B, C, D, E, F, G, H}
a) Contain the string DEF?
b) Contain the strings ABE and EFG?
c)Have D next to C?
d) Contain the strings DCB and BAD?

Consider the following bivariate data.
Point
A
B
C
D
E
F
G
H
I
J
x
4
5
2
6
7
6
2
5
6
5
y
2
6
4
7
7
0
0
1
5
2
(a) Construct a scatter diagram of the given bivariate data. (Do
this on paper. Your instructor may ask you to turn in this
work.)
(b) Calculate the covariance. (Give your answer correct to two
decimal places.)
(c) Calculate sx and sy.
(Give...

Consider the following bivariate data.
Point
A
B
C
D
E
F
G
H
I
J
x
0
1
1
2
3
4
5
6
6
7
y
5
5
8
3
4
1
2
0
1
1
(a) Construct a scatter diagram of the given bivariate data. (Do
this on paper. Your instructor may ask you to turn in this
work.)
(b) Calculate the covariance. (Give your answer correct to two
decimal places.)
(c) Calculate sx and sy.
(Give...

let
A = { a, b, c, d , e, f, g} B = { d, e , f , g}
and C ={ a, b, c, d}
find :
(B n C)’
B’
B n C
(B U C) ‘

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