Linear Algebra Answers

Let  be a linear transformation. Let  and  be zero vectors of  and. Show that

 Use row reduction to determine whether the set of vectors {(1,2,0), (0,1,-1),(1,1,2)} is linearly independent in                                                                 

Show that if A_(n×n) is invertible then the inverse is unique

Use the Gauss-Jordan Elimination method to solve the system of linear equations.

xa + 3xb + xc = 4

2xa + 2xb + xc = -1

2xa + 3xb + xc = 3

Use a single 3x3 matrix A =[ 1 4 3 ]to encode the message “THE COAST IS CLEAR”.

[-2 1 5 ]

[ 2 -1 -4 ]

You are given the system of linear equations

 2x+ky=5,  x+3y=7,

where k

k is a constant.

The system above has no solution when k=

Given a transformation T:R^2→R^2 defined as T(x_1,x_2 )=(0,x_1-x_2). Find ker⁡(T) and R(T), range of T

Given a transformation  defined as. Find  and , range of