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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Subspace of a vector space

Choose difficulty:

Beginner

Intermediate

Advanced

Consider the vector space

R

² over

R

. Its zero is

a: 0 ∈

R

Explanation

Explanation

b: (1, 0) ∈

R

² Explanation

Explanation

c: (0, 1) ∈

R

² Explanation

Explanation

d: (0, 0)∈

R

² Explanation

Explanation

Consider the vector space

M

_2x2 over

R

. Then additive inverse of

X

∈

M

_2x2, is

a:

(-1).X

Explanation

Explanation

b:

X

^-1 Explanation

Explanation

c: Zero matrix Explanation

Explanation

d:

X

Explanation

Explanation

Which of the following planes pass through origin

a:

2x + 3y + 4z = 0

Explanation

Explanation

b:

4x - 2y + z = 7

Explanation

Explanation

c:

3x - 6y = 9

Explanation

Explanation

d:

2(x-1) + (y-2) + (z+3) = 0

Explanation

Explanation

Which of the following equations represent a line passing through origin?

a:

x

² +

y

² = 0 Explanation

Explanation

b:

x + y = x

² Explanation

Explanation

c:

x

= 2 Explanation

Explanation

d:

y = -x

Explanation

Explanation

6(2 , -1) + 3(-1 , 2) equals

a: (9 , 0) Explanation

Explanation

b: (-7 , 1) Explanation

Explanation

c: (5 , 0) Explanation

Explanation

d: (-7 , -1) Explanation

Explanation

For what values

α, β

∈

R

(α + β , α - β) = 3(2 , 4)

a:

α = 9 , β = 3

Explanation

Explanation

b:

α = -6 , β = -3

Explanation

Explanation

c:

α = 9 , β = -3

Explanation

Explanation

d:

α = -6 , β = 0

Explanation

Explanation

For what values

α, β

∈

R

(2 , 6) =

α(1 , 1) + β(1 , -1)

a:

α = 4 , β = -2

Explanation

Explanation

b:

α = -4 , β = -2

Explanation

Explanation

c:

α = 2 , β = -3

Explanation

Explanation

d:

α = -2 , β = 3

Explanation

Explanation

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