Use matrix inversion to solve the collection of systems of linear equations. HINT [See Example 4.] (a) −x − 4y + 2z = −10 x + 2y − z = 11 x + y − z = 14

Step-by-step explanation:

given is a system of linear equations in 3 variables as

This can be represented in matrix form as

AX=B Or

So solution set

X would be

|A|=-1(-1)+4(0)+2(-1)=--1

Cofactors of A are

-1    0    -1

-2   -1     -3

0     1      2

So inverse of A is

1    2   0

0   1     -1  

1     3      -2

Solution set would be

x=12

y=-3

z=-5

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3