New solution: Find a basis for each of the spaces in Exercises 16 through 9 and

Chapter 4, Problem 31

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QUESTION:

Find a basis for each of the spaces in Exercises 16 through 9 and determine its dimension.The space of all 2 x 2 matrices S such that

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QUESTION:

Find a basis for each of the spaces in Exercises 16 through 9 and determine its dimension.The space of all 2 x 2 matrices S such that

ANSWER:

Step 1 of 3

Given that

Let and substitute in the given equation as follows:

We know that if two matrices are equal then then corresponding elements are equal.

By use this, we get the elements as follows:

c=a, d=-b, a=c, and b=-d

The given set is obtained from the matrices which can be written as follows:

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