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.
Answer:
(m³/3 + 5m/2 + 3)pi
Step-by-step explanation:
pi integral [(f(x))² - (g(x))²]
Limits 0 to 1
pi × integral [(2+mx)² - (1-mx)²]
pi × integral[4 + 4mx + m²x² - 1 + 2mx - m²x²]
pi × integral [m²x² + 5mx + 3]
pi × [m²x³/3 + 5mx²/2 + 3x]
Upper limit - lower limit
pi × [m²/3 + 5m/2 + 3]
Verification:
m = 0
[pi × 2² × 1] - [pi × 1² × 1] = 3pi
[m³/3 + 5m/2 + 3]pi
m = 0
3pi
Step-by-step explanation:
Hey there!
By looking at the figure, the given "2x" and "6x + 28" are co-interior angle.
So,
2x + 6x + 28 = 180°. ( sum of co-interior angle is 180°)
8x + 28°=180°
8x = 180° - 28°
8x = 152°
X = 19°
<u>There</u><u>fore</u><u>,</u><u> </u><u>X </u><u>=</u><u> </u><u>1</u><u>9</u><u>°</u><u>.</u>
<em><u>Hope</u></em><em><u> </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
Answer:
1/5 or 0.2
Step-by-step explanation:
-5(p+3/5)=-4
Let's convert 3/5 to decimal form:
-5(p+0.6)=-4
Expand parentheses:
-5p-3=-4
Add -3 to both sides:
-5p=-1
Divide both sides by -5:
p=1/5 or 0.2
Hope this helps!
