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Practice Problems By Easy Worksheet
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1) | Given A is a m × n matrix. Which of the following statements are equivalent? I. Each vector in ℜ ^{n} maps onto a unique vector in ℜ^{m}II. A has no free variables III. The solution to Ax = 0 is always just the zero vector By Easy Worksheet By Easy Worksheet By Easy Worksheet By Easy Worksheet |
2) | Given A is a m × n matrix. Which of the following statements are equivalent? I. Each column has a pivot II. Each vector in ℜ ^{m} is the image of at most one x in ℜ^{n}III. The solution to Ax = 0 is always just the zero vector |

3) | Given A is a m × n matrix. Which of the following statements are equivalent? I. T(x) is one-to-one II. The solution to Ax = 0 is always just the zero vector III. Each column has a pivot By Easy Worksheet By Easy Worksheet By Easy Worksheet By Easy Worksheet |
4) | Given A is a m × n matrix.T(x) = Ax is onto only if it has __ pivot ____ |

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