Question

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.

Answer #1

Here, basically we use some basic properties of the determinants .

Determinant of matrix has a property that:

**" Determinant of any matrix is equal to determinant of
its transpose."**

Thus, desired determinant is 5klm.

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.

Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...

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

Product A is assembled from 6 components. The
components are B, C, D, E, F, G. Components B, D, and F are
purchased from a supplier, complete and ready to assemble.
Component C is assembled from parts H, I, and J. Component E is
assembled from parts K and L. Component G is made in the plant from
raw materials. Part H is made from parts M and N. Part L is made
from parts P, Q, and R. Part...

Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?

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]?

Suppose that L ={F, H, S, T, I, G, E, R} and N = {3, 1, 7}. A
code consists of 3 different symbols selected from L followed by 2
not necessarily different symbols from N. How many different codes
are possible?

Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and
g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g =
{(c, a), (d, e), (e, e), (f, a), (g, g)}
(a) Consider the composed function g ◦ f.
(i) What is the domain of g ◦ f? What is its codomain?
(ii) Find the function g ◦ f. (Find...

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

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...

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