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3 years ago

The ___ of a counting number n, written n!, is the product of the counting number,

Mathematics

1 answer:

Yuki888 [10]3 years ago

6 0

Answer:

Step-by-step explanation:

factorial is the answer

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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

2 is what percent of 12?

REY [17]

Answer:

16.67

Step-by-step explanation:

sana po makatulong

5 0

3 years ago

The Soma Inn is trying to determine its break-even point. The inn has 75 rooms that are rented at $52 a night. Operating costs a

iVinArrow [24]

Answer:

Its Break-even Point. The Inn Has 75 Rooms That Are Rented At $60 A Night. Operating Costs Are As Follows. Salaries Utilities Depreciation Maintenance Maid Service Other Costs $10,600 Per Month 2,400 Per Month 1,500 Per Month 800 Per Month 8 Per Room 34 Per Room Determine The Inn's Break-even Point In ..

Step-by-step explanation:

8 0

3 years ago

A circle has a radius of 3. An arc in this circle has a central angle of 20 degrees.

TiliK225 [7]

Answer:

π/3 units

Step-by-step explanation:

arc length = 2πr(°/360)

= 2π*3(20/360)

= π/3 units

4 0

3 years ago

Without using mathematics tables or calculates simplfy 3/8

Anna007 [38]

Answer:

3/8 CAN ALSO BE WRIITEN AS 375/1000=0.375

SILUTION..

3×125/8×125..

AS WE HAVE TO GET DENOMINATOR IN FORM OF1,10,100,1000,..SO ON.

375/1000

=0.375

7 0

3 years ago