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andrey2020 [161]
3 years ago
10

Find the slope of the line that passes through the two points. (12, 15 ) and (5,7)

Mathematics
1 answer:
maria [59]3 years ago
6 0
Slope of the line that passes through the two point is -2/7
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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
Solve the following quadratic function by utilizing the square root method. f(x) = 1 - x2 x = + [?]
faltersainse [42]

Answer:

Step 1) y=16-x2. Swap the sides so that all terms of the variables are on the left side. Step 2) 16-x_{2}=y. Subtract 16 from both sides. Step 3) -x_{2}=y-16 Divide the two sides by -1. Step 4). \frac{-x_{2}}{-1}=\frac{y-16}{-1} Dividing by -1 undoes the multiplication by -1. Step 5). x_{2}=\frac{y-16}{-1} Step 6) dived y-16 by -1 And the final answer = x_{2}=16-y

Step-by-step explanation:

7 0
2 years ago
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Which is an equation?
liq [111]

Answer:

c

Step-by-step explanation:

because it has an equal sign

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2 years ago
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CAN SOMEONE HELP PLEASE!
tatyana61 [14]
The equation of a cirecle with radius r and center at (h,k) is
(x-h)^2+(y-k)^2=r^2
r=10
center=(-2,-4)
(x+2)^2+(y+4)^2=10^2
(x+2)^2+(y+4)^2=100
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sub given points (or use TI) and see if you get a true statmeent
A is on it

answer is A

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3 years ago
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Can someone help???
OLga [1]
The formula for that is V=\frac{lwh}{3}
but the answer is 4,940cm³ so C.
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