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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Rank and Nullity of linear transformations and matrices

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Let T:R² → R² be the linear transformation defined by T(x, y) = (-x, x), where x, y ∈ R. Then the nullity of T is?

a: 0 Explanation

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b: 1 Explanation

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c: 2 Explanation

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d: 4 Explanation

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Let T:R² → R² be the linear transformation defined by T(x, y) = (-x, -y), where x, y ∈ R. Then the rank of T is?

a: 1 Explanation

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b: 0 Explanation

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c: 2 Explanation

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d: 4 Explanation

Explanation

Let T:R² → R³ be the linear transformation defined by T(x, y)= (x, x+y, 0), where x, y, z ∈ R. Then the nullity of T is?

a: 0 Explanation

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b: 1 Explanation

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c: 2 Explanation

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d: 3 Explanation

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Let T:R² → R³ be the linear transformation defined by T(x, y) = (-x, -y, 0), where x, y, z ∈ R. Then the null space of T is?

a: {(0, 0, γ): γ ∈ R} Explanation

Explanation

b: {(α, β, 0): α, β ∈ R} Explanation

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c: {(α, 0, γ): α, γ ∈ R} Explanation

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d: {(0, 0, 0)} Explanation

Explanation

Let T:R² → R² be the linear transformation defined by T(x, y)=(x, y), where x, y ∈ R. Then the range of T is?

a: {(α, β): α, β ∈ R} Explanation

Explanation

b: {(α, 0): α ∈ R} Explanation

Explanation

c: {(0, β): β ∈ R} Explanation

Explanation

d: {(0, 0)} Explanation

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