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kirill115 [55]
2 years ago
11

True or False?

Mathematics
1 answer:
stira [4]2 years ago
6 0

In a situation where x is a nontrivial solution, then every entry in x should not be nonzero. Therefore, it's false.

<h3>What is a nontrivial solution?</h3>

A nontrivial solution simply means a system of equation where the determinant of the coefficient is zero. When x is a nontrivial solution of Ax = 0, then at least one entry should be nonzero.

The equation x= x2u + x3v, with x2 and x3 free (and neither u nor v a multiple of the other), describes a plane through the origin. This is true. Since they're free variables, the space span has dimensions and this spans through the origin.

The equation Ax = b is homogeneous if the zero vector is a solution. Since x = 0 is a solution. Therefore, Ax = b. Hence, b = 0.

The effect of adding p to a vector is to move the vector in a direction parallel to p. It should be noted that adding p to a vector moves it in a direction that's parallel.

Learn more about nontrivial solution on:

brainly.com/question/15120462

You might be interested in
Which relationship describes angles 1 and 2? Select each correct answer. A adjacent angles B complementary angles C vertical ang
Scrat [10]
The correct answer for this question is this one:
<span>- A adjacent angles
-D supplementary angles

The relationship that describes angle 1 and angle 2 is that they are adjacent angles -- at the same time they are also supplementary angles.</span>
Hope this helps answer your question and have a nice day ahead.
3 0
2 years ago
Read 2 more answers
1.) What are the zeros of the polynomial? f(x)=x^4-x^3-16x^2+4x+48.
Lerok [7]

Answer:

3.) \displaystyle [x - 2][x^2 + 2][x + 4]

2.) \displaystyle 2\:complex\:solutions → x^2 + 3x + 6 >> -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2}

1.) \displaystyle 4, -3, 2, and\:-2

Step-by-step explanation:

3.) By the Rational Root Theorem, we would take the Least Common Divisor [LCD] between the leading coefficient of 1, and the initial value of −16, which is 1, but we will take 2 since it is the <em>fourth root</em> of 16; so this automatically makes our first factor of \displaystyle x - 2.Next, since the factor\divisor is in the form of \displaystyle x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

2| 1 2 −6 4 −16

↓ 2 8 4 16

__________________

1 4 2 8 0 → \displaystyle x^3 + 4x^2 + 2x + 8

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x⁴ + 2x³ - 6x² + 4x - 16]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x³, the 4x² follows right behind it, bringing 2x right up against it, and bringing up the rear, 8, giving you the quotient of \displaystyle x^3 + 4x^2 + 2x + 8.

However, we are not finished yet. This is our first quotient. The next step, while still using the Rational Root Theorem with our first quotient, is to take the Least Common Divisor [LCD] of the leading coefficient of 1, and the initial value of 8, which is −4, so this makes our next factor of \displaystyle x + 4.Then again, we use Synthetic Division because \displaystyle x + 4is in the form of \displaystyle x - c:

−4| 1 4 2 8

↓ −4 0 −8

_____________

1 0 2 0 → \displaystyle x^2 + 2

So altogether, we have our four factors of \displaystyle [x^2 + 2][x + 4][x - 2].

__________________________________________________________

2.) By the Rational Root Theorem again, this time, we will take −1, since the leading coefficient & variable\degree and the initial value do not share any common divisors other than the <em>special</em><em> </em><em>number</em> of 1, and it does not matter which integer of 1 you take first. This gives a factor of \displaystyle x + 1.Then start up Synthetic Division again:

−1| 1 3 5 −3 −6

↓ −1 −2 −3 6

__________________

1 2 3 −6 0 → \displaystyle x^3 + 2x^2 + 3x - 6

Now we take the other integer of 1 to get the other factor of \displaystyle x - 1,then repeat the process of Synthetic Division:

1| 1 2 3 −6

↓ 1 3 6

_____________

1 3 6 0 → \displaystyle x^2 + 3x + 6

So altogether, we have our three factors of \displaystyle [x - 1][x^2 + 3x + 6][x + 1].

Hold it now! Notice that \displaystyle x^2 + 3x + 6is unfactorable. Therefore, we have to apply the Quadratic Formula to get our two complex solutions, \displaystyle a + bi[or zeros in this matter]:

\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = x \\ \\ -3 ± \frac{\sqrt{3^2 - 4[1][6]}}{2[1]} = x \\ \\ -3 ± \frac{\sqrt{9 - 24}}{2} = x \\ \\ -3 ± \frac{\sqrt{-15}}{2} = x \\ \\ -3 ± i\frac{\sqrt{15}}{2} = x \\ \\ -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2} = x

__________________________________________________________

1.) By the Rational Root Theorem one more time, this time, we will take 4 since the initial value is 48 and that 4 is the root of the polynomial. This gives our automatic factor of \displaystyle x - 4.Then start up Synthetic Division again:

4| 1 −1 −16 4 48

↓ 4 12 −16 −48

___________________

1 3 −4 −12 0 → \displaystyle x^3 + 3x^2 - 4x - 12

We can then take −3 since it is a root of this polynomial, giving us the factor of \displaystyle x + 3:

−3| 1 3 −4 −12

↓ −3 0 12

_______________

1 0 −4 0 → \displaystyle x^2 - 4 >> [x - 2][x + 2]

So altogether, we have our four factors of \displaystyle [x - 2][x + 3][x + 2][x - 4],and when set to equal zero, you will get \displaystyle 4, -3, 2, and\:-2.

I am delighted to assist you anytime.

3 0
3 years ago
Solve for x: 2|x − 3| + 1 = 7 (5 points) x = 0, x = 6 x = −1, x = 6 x = 0, x = 9 No solutions
Dominik [7]
2|x-3|+1=7
2|x-3|=6
|x-3|=3

x-3 = 3 or x-3 = -3
x=0 or 6
8 0
3 years ago
Read 2 more answers
If a population mean is 300 and the sample mean is 400, the difference of 100 is called:
rodikova [14]

Answer:

B. Sample error.

Step-by-step explanation:

Such type of error is called Sample error.

Sample error occurs when

Sample error is a statistical error when an expert fails to choose a sample which symbolizes the whole data population and the outcomes of the sample do not reflect the outcomes from the whole population.

7 0
2 years ago
Parallel or perpendicular 3x+5y=10 and 5x-3y=-6
devlian [24]
3x+5y=10 and 5x-3y=-6 is perpendicular.
6 0
2 years ago
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