Virtual Labs

Let

T:R

ⁿ→

R

ⁿ be the one-to-one onto linear transformation and let

T(X)=b, b

∈

R

ⁿ, be a linear map equation. Then it has

a: One and only one solution Explanation

Explanation

b: Infinitely many solutions Explanation

Explanation

c: More than one solution Explanation

Explanation

d: No solution Explanation

Explanation

Let

T:R

³→

R

² be the linear transformation defined by

T(x, y, z)=(x, y+z),

where

x, y, z∈R

. Consider the linear map equation

T(X)=b

, where

b=(1, 0)

. Then

a: Solution exists and there are infinitely many solutions Explanation

Explanation

b: Solution exists and there are finite but more than one solutions Explanation

Explanation

c: Unique solution Explanation

Explanation

d: System is inconsistent Explanation

Explanation

Let

T:R

²→

R

³ be the linear transformation defined by

T(x, y)=(x, x+y, x-y)

, where

x, y∈R

. Consider the linear map equation

T(X)=b

, where

b=(1, 0, 0)

. Then

a: Solution exists and there are infinitely many solutions Explanation

Explanation

b: Solution exists and there are finite but more than one number of solution Explanation

Explanation

c: Unique solution Explanation

Explanation

d: System is inconsistent Explanation

Explanation

Let

T:R

²→

R

² be the linear transformation defined by

T(x, y)=(3x, 4x)

, where

x, y∈R

and let

b=(3, 4)

. Then which of following is a solution of the linear map equation

T(X)=b

x=0, y=0

Explanation

x=-1, y=1

Explanation

x=1, y=-54

Explanation

d: None of the above Explanation

Explanation

Let

T:R

²→

R

² be the linear transformation defined by

T(x, y)=(y, 0)

, where

x, y∈R

. Let the statements

A

and

B

be as given below:

A

: The linear map equation

T(X)=(1, 4)

is consistent.

B

: The linear map equation

T(X)=(4, 0)

is consistent. Then which of following holds

A

is true,

B

is false Explanation

Explanation

A

is false,

B

is true Explanation

Explanation

A

is true,

B

is true Explanation

Explanation

A

is false,

B

is false Explanation

Explanation

Linear map equation and its solution