Pls help with this math question

A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

3 years ago

Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 121212 feet^3 3 start superscrip

Dahasolnce [82]

Answer:

The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?

The length of the pillow is 4 feet

Step-by-step explanation:

The formula of the volume of the wedge is $V=\frac{1}{2}bhl$ , where

b is the base of it
h is the height of it
l is the length of it

∵ The pillow in the shape of a wedge

∵ The pillow is filled with 12 ft³ of fluffy material

∴ The volume of the wedge = 12 ft³

∵ The base = 3 feet

∵ The height = 2 feet

- Use the formula of the volume above to find its length

∵ $V=\frac{1}{2}(2)(3)l$

∴ V = 3 l

∵ V = 12 ft³

- Equate 3 l by 12

∴ 3 l = 12

- Divide both sides by 3

∴ l = 4 feet

∴ The length of the pillow is 4 feet

8 0

3 years ago

Change 52.7kobo to naira

EastWind [94]

Answer:

442.590884 naira(NGN)

Step-by-step explanation:

1 kobocoin=8.413029 naira(NGN)

8 0

3 years ago

A factory producing cell phones has the following cost and revenue functions: ()=2+75+2,688 C ( x ) = x 2 + 75 x + 2 , 688 and (

prisoha [69]

Answer:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

Step-by-step explanation:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

6 0

2 years ago

What is <br> 2n - 3 = 9 ( solve the equation)

BartSMP [9]

$2n - 3 = 9 \\ 2n = 12 \\ n = 6$

5 0

3 years ago