Chapter 4 Problem 9 Previous Problem List Next 14 is a basis

Chapter 4: Problem 9 Previous Problem List Next -14 is a basis for R2. Find the coordinates of the vector x with respect to the basis B: (1 point) The set B Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor Page generated at 17 at 08:05pm MST WeBwork o 1996-2016 l theme: math4 Iww version: 2.11 lpg version: 2.11IThe WeBWork Project

Solution

Let A =

-2

-4

-14

-4

2

-8

We will reduce A to its RREF as under:

Multiply the 1st row by -1/2

Add 4 times the 1st row to the 2nd row

Multiply the 2nd row by 1/10

Add -2 times the 2nd row to the 1st row

Then the RREF of A is

1

0

3

0

1

2

Hence x = (-14,-8)^T = 3(-2,-4)^T +2(-4,2)^T. The coordinates of x with respect to the basis B are( 3,2)

-2	-4	-14
-4	2	-8