Linear Algebra Answers

A bookstore placed two orders with a publisher. The first order was for 12 copies of a history text
and 4 copies of a geography text, for a total cost of $1060. The second order was for 6 copies of the
history text and 4 copies of the geography text for a total cost was $640.

a) What is the cost of one copy of the history text?

b) What is the cost of one copy of the geography text?

1) Translate the verbal description into a system of equations then solve.

(a) Find two numbers whose sum is 102 and one number is twice the other number.
(b) The sum of three times the first number and the second number is one. The first number minus the second number is seven.

2) Solve the system of equations

(a) y=−x
5x−7y=6
(b) 2x+3y=15
5x+4y=−1
(c) y=−x
5x−7y=6

please & thank you

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Solve for c

1. Show that: [ x l m 1]
[ a x n 1] = (x-a)(x-b)(x-c)
[ a b x 1]
[ a b c 1]

2. Show that: [ 1+ (a)^2 - (b)^2 2b -2b ]
[ 2ab 1 - (a)^2 + (b)^2 2a ]
[ 2b -2(a)^2 1 - (a)^2 - (b)^2 ]
is a perfect cube.

{please note that these are determinants, the first one is a 4X4 determinant and the second one is a 3X3 determinant}

a) Find the inverse of the matrix











−
−
=
1 2 2
1 2 4
1 1 1
A
using Gauss-Jordon method.

Solve the system of equations
12 10x1 + x2 + x3 =
12 10 x1 + x2 + x3 =
12 10 x1 + x2 + x3 =
using Gauss-Jordon method with pivoting.

Use the properties of determinants to evaluate the following determinant: (5)
(b + c)
2
a
2
a
2
b
2
(c + a)
2
b
2
c
2
c
2
(a + b

Consider the following system of equations:
x
1 3x
2 x
3 = 3
x
1 + 5x
2 + 3x
3 = 1
x
1 + 7x
2 + 3x
3 = 1
Check whether the system of equations have a solution or not

Let T : R^2 -> R^2 and S: R^2 -> R^2 be linear operators defined by
T ( x(subscript1) , x(subscript2) ) = (x(subscript1) + x(subscript2) , x(subscript1) - x(subscript2)) and S( x(subscript1) , x(subscript2) ) = ( x(subscript1) , x(subscript1) + 2x(subscript2) )
respectively.
i) Find ToS and SoT.
ii) Let B ={ (1;0) , (0;1) } be the standard basis of R^3. Verify that
[ToS](subscriptB) = [T](subscriptB) o [S](subscriptB).

solve the set of linear equation a+2b+3c=5,3a-b+2c=8,4a-6b-4c=2 find c