Answer:
Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.
If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.
Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.
Answer: 
This is the same as writing (n-m)/n
Don't forget about the parenthesis if you go with the second option.
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Explanation:
The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.
For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.
The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.
We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".
Doing a bit of algebra would have these steps

and now the expression is one single fraction.
Answer:
the common difference is 6.
Step-by-step explanation:
Given;
first term of an AP, a = -7
let the common difference = d
The third term is written as;
T₃ = a + 2d
The eight term is written as;
T₈ = a + 7d
The ratio of the eight term to third term = 7:1

Therefore, the common difference is 6.
I will not be able to explain but you can surely trust those answers
A = 130
B = 50
C = 50
D = 130
E = 75
F = 105
G = 105
H = 75
I = 40
J = 140
K = 38
L = 102
M = 38
N = 50
O = 95
P = 35
Q = 130
R = 100
S = 100
T = 80
U = 80
V = 35
W = 45
X = 40
Y = 40
Z = 60
Answer:
V=129659.9491≈129659.95
Step-by-step explanation: