Matrix transformation problem

In summary, the problem is asking to find all values of x in R4 that when multiplied by A, result in the zero vector. After row reduction, the only restriction is that x4 must be equal to 0, while the values of x1, x2 and x3 can be arbitrary.
  • #1
beanryu
92
0
please help
find all x in R4 that are mapped into teh zero vector by A
A =
1 3 9 2
1 0 -4 3
0 1 2 3
-2 3 0 5

i think the problem wants me to find x where x times A = 0

so i did this augmented matrix
A=
1 3 9 2 0
1 0 -4 3 0
0 1 2 3 0
-2 3 0 5 0

then, after row reduction and stuff, i got this

1 0 3 0 0
0 1 2 0 0
0 0 0 1 0
0 0 0 1 0

all i know is x4 = 0... it doesn't seem to give anything about x1 x2 and x3... are their values arbitrary or am I wrong?

thank you.
 
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  • #2
The values of x1, x2 and x3 are arbitrary. You can assign any values to them and it will still satisfy the equation xA = 0.
 

1. What is a matrix transformation problem?

A matrix transformation problem involves transforming a matrix into a new matrix using a set of rules or operations.

2. What are some common matrix transformations?

Common matrix transformations include scaling, rotation, shearing, and translation.

3. How do you perform a matrix transformation?

To perform a matrix transformation, you first need to define the transformation matrix. Then, you multiply the transformation matrix by the original matrix to get the transformed matrix.

4. Can you give an example of a matrix transformation?

One example of a matrix transformation is scaling a 2D object by a factor of 2. This can be done by multiplying the original matrix by the transformation matrix [2 0; 0 2].

5. How are matrix transformations used in real life?

Matrix transformations are used in various fields such as computer graphics, robotics, and physics. They are used to manipulate and transform objects in a 2D or 3D space, allowing for more realistic and accurate simulations and models.

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