Let's consider an arbitrary 2x2 matrix as an example,
The columns of
are linearly independent if and only if the column vectors
are linearly independent.
This is the case if the only way we can make a linear combination of
reduce to the zero vector is to multiply the vectors by 0; that is,
only by letting
.
A more concrete example: suppose
Here,
and
. Notice that we can get the zero vector by taking
and
:
so the columns of
are not linearly independent, or linearly dependent.
Answer:
k = 4 units
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
k² + 7.5² = 8.5²
k² + 56.25 = 72.25 ( subtract 56.25 from both sides )
k² = 16 ( take the square root of both sides )
k = 
= 4
We know that
case 1) -10/-7-----> 10/7-------> is not <span>equivalent to -10/7
case 2) </span>-3 1/7----> (-3*7+1)/7----> -20/7 ------> is not equivalent to -10/7
case 3) 1 3/7-----> (1*7+3)/7----> 10/7 ------> is not equivalent to -10/7
case 4) - -10/-7---> +10/-7----> -10/7------> is equivalent to -10/7
case 5) -1 3/7----> (-1*7+3)/7----> -4/7 ------> is not equivalent to -10/7
the answer is
- -10/-7
Nice
area=pir^2
the areas are
pir^2+pi(2r)^2
they add to 8pi
8pi=pir^2+pi(2r)^2
undistribute pi
8pi=pi(r^2+(2r)^2)
divide both sides by pi
8=r^2+(2r)^2
expand
8=r^2+4r^2
add
8=5r^2
divide by 5
8/5=r^2
sqrt both sides
√(8/5)=r
double since it is double
2√(8/5) is radius of bigger aka (4√10)/5
radius=(4√10)/5
Answer is C.
All real numbers
hope it helps
