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:
x=6
Step-by-step explanation:
The inverse is the equation with the x and y variables transposed
Answer:
-76-43i
Step-by-step explanation:
First expand the multiplied terms
8-3i-(64+64i-24i+24)
8-3i-(64+40i+24)
Simplify
8-3i-64-40i-24
-76-43i
Answer:
The answer SHOULD be 7/8=224/x;256 pounds.
You may have made a mistake in inputting it here on Brainly. So look for the one that matches that.
Step-by-step explanation:
This is what we know:
Jasper = 224 pounds
Balin = x
Jasper = 7/8 of x
Now we make an equation for that:

To match the selections we will isolate 7/8 on one side of the equation:

Using ratio and proportion we can solve for what x is. Multiply 224 by 8 and divide it by 7. Or you can do it this way too:




So x = 256 pounds
Answer:
- D. Because <1 and <2 are each supplementary to <3, they are therefore congruent
Step-by-step explanation:
A. m<1 + m<2 + m<3 + m<4 = 360
- Incorrect in terms of the proof
B. The sum of the measures of angles of a triangle is 180°
C. The measure of all right is 90°
D. Because <1 and <2 are each supplementary to <3, they are therefore congruent