What is the dimension of the solution space for Ax=0 with A as a 2x3 matrix?

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Start date Nov 5, 2007
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Dimension Space

In summary, the dimension of solution space refers to the number of independent variables or parameters needed to fully define a solution to a problem. It is determined by the number of equations or constraints and can change depending on the complexity of the problem. The dimension is important in understanding problem complexity and the number of variables to consider, and it relates to linear algebra by representing the number of linearly independent vectors in a vector space.

Nov 5, 2007

eyehategod

Find the dimensions of the soultion space of Ax=0,
where A=
1 2 5
–1 3 1
(A is a 2x3 matrix).

To find the dimension you have to subtract n from rank(A)
//n being the number of columns

3-2=1
The dimension of the solution space is 1. is this correct?

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Nov 5, 2007

Galileo

Science Advisor

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Yup.

1) What is the "dimension of solution space"?

The dimension of solution space refers to the number of independent variables or parameters that are required to fully define a solution to a given problem.

2) How is the dimension of solution space determined?

The dimension of solution space is determined by the number of equations or constraints that need to be satisfied in order to find a solution. Each independent variable or parameter corresponds to one dimension.

3) Can the dimension of solution space change?

Yes, the dimension of solution space can change depending on the complexity of the problem and the number of variables or constraints involved. It can also change if the problem is simplified or if new information is added.

4) Why is the dimension of solution space important?

The dimension of solution space is important because it helps us understand the complexity of a problem and the number of variables that need to be considered in order to find a solution. It also helps us determine if a problem has a unique solution or if there are multiple possible solutions.

5) How does the dimension of solution space relate to linear algebra?

In linear algebra, the dimension of a vector space is equivalent to the dimension of solution space. This means that the number of linearly independent vectors in a vector space is equal to the number of independent variables in the solution space.