IITM BS Question 23 - Week 3 Practice

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IITM BS Question 23 - Week 3 Practice | Prasnya

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Q23Numerical2 Marks16 Oct 2022

Consider the statements:

P

V=\mathbb{R}^2

with addition

(x_1,y_1)+(x_2,y_2)=(x_1x_2,y_1y_2)

and scalar multiplication

c(x,y)=(cx,cy)

is a vector space.

Q

: Let

V

be a vector space. If

u,v,w\in V

are such that

au+bv+cw=0

for some scalars

a,b,c\in\mathbb{R}

and

ac\ne0

, then

\operatorname{span}\{u,v\}=\operatorname{span}\{v,w\}

. Statement 1:

P

is true, but

Q

is false. Statement 2:

Q

is true, but

P

is false. Statement 3: Both

P

and

Q

are true. Statement 4: Both

P

and

Q

are false. Which statement is correct? Enter its serial number.

Your answer

Press Enter to check.

Q23

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16 Oct 2022

Mathematics 2 · Week 3

Q23.Consider the statements:

P

V=\mathbb{R}^2

with addition

(x_1,y_1)+(x_2,y_2)=(x_1x_2,y_1y_2)

and scalar multiplication

c(x,y)=(cx,cy)

is a vector space.

Q

: Let

V

be a vector space. If

u,v,w\in V

are such that

au+bv+cw=0

for some scalars

a,b,c\in\mathbb{R}

and

ac\ne0

, then

\operatorname{span}\{u,v\}=\operatorname{span}\{v,w\}

. Statement 1:

P

is true, but

Q

is false. Statement 2:

Q

is true, but

P

is false. Statement 3: Both

P

and

Q

are true. Statement 4: Both

P

and

Q

are false. Which statement is correct? Enter its serial number.

Your Answer

Save

Check

Details