Term
| How do you find the column space of A? |
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Definition
| The column space of A is the set of all b for which the system has a solution |
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Term
| How do you create an explicit description of Nul A? |
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Definition
| To create an explicit description of Nul A, solve the equation Ax = 0 and write the solution in parametric vector form. |
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Term
| What is the standard basis for R^n? |
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Definition
| The set {e1,...,en} is the standard basis for R^n. |
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Term
| How do you find a basis for the null space of a matrix? |
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Definition
| If the matrix is A, solve Ax = 0 by creating an augmented matrix and row reducing. Then write your answer in parametric vector form. Once in parametric vector form, the vectors that are left (pivot columns) form basis for Nul A which is automatically linearly independent. |
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