Not necessarily.
and
may be linearly dependent, so that their span forms a subspace of
that does not contain every vector in
.
For example, we could have
and
. Any vector
of the form
, where
, is impossible to obtain as a linear combination of these
and
, since
unless
and
.
Answer:
1. No solution
2. Infinite solutions
Step-by-step explanation:
1. To solve the system, set the equations equal to each other and solve for x.
2x - 5 = 2x + 7
-5 = 7
This is a false statement. This means there is no solution.
2. To solve the system, graph each equation.
y = -3/4 x - 5/2 has a y-intercept -5/2 and slope -3/4.
3x + 4y = -10 converts to y = -3/4x -5/2.
This graphs as the exact same line. This system has infinite solutions.
Answer:Alden is 13 years old
Step-by-step explanation
Let x represent Alden's age.
Let y represent the age of his sister.
Let z represent the age of his second sister.
His sister is 5 years older than he is and 3 times as old as his second sister. This means that
y = x + 5
y = 3z
Alden's brother is 4 years younger than his second sister. It means that his brother's age is
z - 4
His brother is 2. It means that
z - 4 = 2
z = 2 + 4 = 6
y = 3z
y = 3 × 6 = 18
Substituting y = 18 into y = x + 5, it becomes
18 = x + 5
x = 18 - 5 = 13
Answer:
The area of the rectangle in polynomial form is 
Step-by-step explanation:
Given
Shape: Rectangle
Required
Area of the rectangle
The area of a rectangle is calculated as thus;
By substituting 
for height and 
for width; This gives
Expand the bracket
Open each bracket
Hence, the area of the rectangle in polynomial form is
Answer:
7
Step-by-step explanation:
