Because even though 'a' and 'b' are rational, and their squares are
also rational, that doesn't guarantee that the sum of their squares
has a rational square root.
Examples:
1 and 2
Sum of squares = 5
√5 is irrational
2 and 3
Sum of squares = 13
√13 is irrational
4 and 5
Sum of squares is 41
√41 is irrational
'c' is rational only when 'a', 'b', and 'c' form a . . . . . wait for it . . . . .
a 'Pythagorean triple'.
Examples:
3 and 4
Sum of squares is 25
√25 = 5 is rational yay
5 and 12
Sum of squares is 169
√169 = 13 is rational yay
Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
The answer is
Logarithm both sides of the equation:
Since:
, then:
Back to our equation:
Answer:
75%
Step-by-step explanation:
There are 6 numbers that fit the rule, 1, 2, 3, 4, 6, 8. Since there are a total of 8 numbers, there is a 6/8 chance picking one or 75% chance.
Answer: 29, 30, 35, 36
Step-by-step explanation:
As per your info about first page.
The paper containing 64 has following other pages
On the back of 29, it is 30. The pages are such that for each page p, 65-p will be also on the same page.
Then,
65-29= 36
65-30 = 35
So the four pages in this sheet are 29, 30, 35, 36.
