Question

Section 1.3 The Intersection Point of a Pair of Lines

Solve the systems of linear equations

- ! ) 4( ? ? + + 2? ) ( ? = = 3
- !? ? − + - ( 2? ? = = 4 6

Answer #1

**1.** Given system of equation ,

......(i)

......(ii)

Substituting in equatio (i) we get ,

Or ,

Or ,

Hence the required intersection point is .

**2.** Given system of equation ,

......(iii)

........(iv)

Substituting in (iii) we get ,

or ,

Or ,

Hence the required intersection point is .

**N.B :** I wish I have written the equations
correctly , if it is not let me know in comment box
. .

Use Gauss-Jordan elimination to solve the following systems of
linear equations, or state that there are no solutions.
a)
4?+8?=−4
−3?−6?=5
b)
?+4?−?=8
2?+8?+?=1
you should find that the system has infinitely many solutions.
Introduce a parameter in order to give the general solution. Then
give one particular solution.

Use MATLAB to determine the intersection point for the sets of
equations shown below. Use the backslash when possible. Graph the
equations with different colors, and plot the intersection point
with a red star marker. If the equations do not intersect, graph
them anyway. Include a legend.
cannot use 'ezplot' or 'solve'
b) -4(x1)+(2(x2))^3=10 x1+x2=-8

Solve the following system of linear equations using the
techniques discussed in this section. (If the system is dependent
assign the free variable the parameter t. If the system is
inconsistent, enter INCONSISTENT.)
x1 −
x3
=
−4
2x2 −
x4
=
0
x1 − 2x2
+ x3
=
0
−x3 +
x4
=
2
(x1, x2,
x3,
x4)

in parts a and b use gaussian elimination to solve the systems
of linear equations. show all steps.
a. x1 - 4x2 - x3 + x4 = 3
3x1 - 12 x2 - 3x4 = 12
2x1 - 8x2 + 4x3 - 10x4 = 12
b. x1 + x2 + x3 - x4 = 2
2x1 + 2x2 - 2x3 = 3
2x1 + 2x2 - x4 = 2

Solving Systems of Linear Equations Using Linear
Transformations
In problems 2 and 5 find a basis for the solution set of the
homogeneous linear systems.
2. ?1 + ?2 + ?3 = 0
?1 − ?2 − ?3 = 0
5. ?1 + 2?2 − 2?3 + ?4 = 0
?1 − 2?2 + 2?3 + ?4 = 0.
So I'm in a Linear Algebra class at the moment, and the
professor wants us to work through our homework using...

Examine whether or not these pair of lines are perpendicular to
each other. (1) y - 3x - 2 = 0 and 3y + x + 9 = 0 (2) 3y - 4 = 2x +
3 and y-5 = x+ 6 (3) Find the equations of the tangent and normal
to the curve xsquare + ysquare+3xy-11 = 0 at the point x = 1, y =
2.

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations. Indicate whether
the system has a unique solution, infinitely many solutions, or no
solution. Clearly write the row operations you use. (a) (5 points)
x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y
+ z = 4 3x − 5y + 3z = 13 3y − 3z =...

How can graphing methods be used to solve a system of linear
equations, and how can you determine the equations of the two lines
by analyzing the graph?

How can graphing methods be used to solve a system of linear
equations, and how can you determine the equations of the two lines
by analyzing the graph?

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations.
Indicate whether the system has a unique solution, infinitely many
solutions, or no solution. Clearly write
the row operations you use.
(a)
x − 2y + z = 8
2x − 3y + 2z = 23
− 5y + 5z = 25
(b)
x + y + z = 6
2x − y − z = 3
x + 2y + 2z = 0

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