Linear Algebra Answers

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                                                                

A parabola "y=ax^{2}+bx+c"  passes through the points (-2, 10); (1,4) and (2,6).

Which of the following are correct? More than one answer may be correct

1. The augmented matrix for the system of equations connecting a, b and c is "\\left(\\begin{array}{cccc}4&-2&1&:&10\\\\1&1&1&:&4\\\\4&2&1&: &6\\end{array}\\right)"
2. The determinant of the coefficient matrix for the system of equations connecting a, b and c is -12.
3. The parabola above passes through the origin.
4. By applying Gauss elimination, the normal form of the augmented matrix for the system of equations connecting a, b and c is"\\left(\\begin{array}{cccc}1&0&0&:&1\\\\0&1&0&:&-1\\\\0&0&1&: &4\\end{array}\\right).\n\n\u200b"

A system of linear equations has the augmented matrix

"\\left(\\begin{array}{cccc}1&1&k&:&1\\\\-1&1&2k&:&-3\\\\k&1&1&: &k+1\\end{array}\\right)"

where k

k is a constant. What is the value of k such that the system above has no solution?

1. "k=-1"
2. "k=-2"
3. "k=0"
4. "k=1"