Select the correct answer.

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

is

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

3 years ago

I need to know how to balance the scales it says ''Make the scales balance by using addition and subtraction to find in the miss

kramer

This would be much, much, much easier if you told us
what numbers you do have on each side of the scale now.

The idea (probably) is that the scale is balanced when
the numbers add up to the same amount on both sides.

So you need to put some numbers in the blanks that will either
add more to the side that has less, or subtract some from the side
that has more, to make both sides equal.

6 0

2 years ago

what do the following two equations represent? please help 4x+2y= 10 4x-2y= -10 a) the same line b) distance parallel lines c) p

Lady bird [3.3K]

Answer:

D

Step-by-step explanation:

The equations are

● 4x + 2y = 10 (1)

● 4x - 2y = -10 (2)

● 4x + 2y = 10

Add - 4x to both sides

● 4x + 2y -4x = 10 -4x

● 2y = 10 -4x

Divide both sides by 2

● 2y/2 = (10 - 4x)/2

● y = 5 - 2x

● y = -2x + 5 (1)

● 4x - 2y = -10

Add -4x to both sides

● 4x -2y -4x = -10 - 4x

● -2y = -10 - 4x

Divide both sides by -2

● -2y/-2 = (-10 -4x)/-2

● y = 10 + 2x

● y = 2x + 5 (2)

So the equation are

● y = 2x + 5

● y = -2x + 5

Graph them

The lines intersect at (0,5) but aren't perpendicular

So the answer is d

8 0

3 years ago

Suppose each of 12 players rolls a pair of dice 3 times. Find the probability that at least 4 of the players will roll doubles a

polet [3.4K]

Answer:

Our answer is 0.8172

Step-by-step explanation:

P(doubles on a single roll of pair of dice) =(6/36) =1/6

therefore P(in 3 rolls of pair of dice at least one doubles)=1-P(none of roll shows a double)

=1-(1-1/6)3 =91/216

for 12 players this follows binomial distribution with parameter n=12 and p=91/216

probability that at least 4 of the players will get “doubles” at least once =P(X>=4)

=1-(P(X<=3)

=1-((₁₂ C0)×(91/216)⁰(125/216)¹²+(₁₂ C1)×(91/216)¹(125/216)¹¹+(₁₂ C2)×(91/216)²(125/216)¹⁰+(₁₂ C3)×(91/216)³(125/216)⁹)

=1-0.1828

=0.8172

7 0

3 years ago

Jill has been watching the squirrels that live in her neighborhood. The number of squirrels changes each week. n f(n). 1 8. 2 12

qaws [65]

Answer: D) $f(n)=8(1.5)^{n-1}$

Step-by-step explanation:

From the given table we can see that this is not representing a linear function as the rate of change is not constant.

So it can be exponential growth function $A(b)^{n-1}$ , where A is the initial amount , b is the multiplicative rate of growth and n is the time period in weeks.

Now here at n=1 , f(n)=8

Therefore, A=8

Now, for n=2

$f(2)=8(b)^{2-1}\\\Rightarrow12=8b\\\Rightarrow\ b=\frac{12}{8}\\\Rightarrow\ b=1.5$

By substitute the values of A and b in the above equation, we get the equation $f(n)=8(1.5)^{n-1}$

Therefore, the function best shows the relationship between n and f(n) is

$f(n)=8(1.5)^{n-1}$ , where n is the number of weeks.

7 0

2 years ago

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