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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Linear Transformation and Matrices

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Intermediate

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Let

T:R

²→

R

² be the linear transformation defined by

T

(

x

,

y

)=(

x

, 0), where

x

,

y

∈

R

. Then the nullity of

T

is?

a: 1 Explanation

Explanation

b: 0 Explanation

Explanation

c: 2 Explanation

Explanation

d: 3 Explanation

Explanation

Let

T:R

²→

R

² be the linear transformation defined by

T(x,

y)=(x,

-y)

, where

x,

y

∈

R

. Then the rank of

T

is?

a: 1 Explanation

Explanation

b: 0 Explanation

Explanation

c: 2 Explanation

Explanation

d: 3 Explanation

Explanation

Let

T:R

²→

R

³ 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: 1 Explanation

Explanation

b: 0 Explanation

Explanation

c: 2 Explanation

Explanation

d: 3 Explanation

Explanation

Let

T:R

²→

R

³ 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

Explanation

c: {(α, 0, γ): α, γ ∈

R

} Explanation

Explanation

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

Explanation

Let

T:R

²→

R

² be the linear transformation defined by

T(x,

y)=(x,

y)

, where

x,

y

∈

R

. Then the range space 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

Explanation

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