I think the answere is $67
Answer:
(A) Set A is linearly independent and spans
. Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors
, we are to decide which of the given statements is true:
In Matrix
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans
. Thus it is basis for
.
Answer:
x = 2
Step-by-step explanation:
4(2x - 1) = 3x + 6
Simplify
8x - 4 = 3x + 6
Subtract 3x from both sides
8x - 3x - 4 = 3x - 3x + 6
5x - 4 = 6
Add 4 to both sides
5x - 4 + 4 = 6 + 4
5x = 10
Divide both sides by 5
5x/5 = 10/5
x = 2
Answer: y= 3x-1
Step-by-step explanation:
Equation of a straight line:
y = mx + b ------(i)
Step by Step Solution:
Step 1: Calculating Slope (m).
m =
y2-y1
x2-x1
m =
2--1
1-0
m =
3
1
m = 3
Now putting value of m in equation (i)
y = 3x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (0,-1) for calculating y-intercept:
y = mx + b
-1 = 3(0) + b
-1 = 0 + b
-1 = b
b = -1
2/3
16/24 and divide the greatest common factor (8)