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3 years ago

1. Find a vector in R^3 which is not in the span of the set S-((1,2, -2), (2, -1, 1). Explain.

Mathematics

1 answer:

pav-90 [236]3 years ago

8 0

Answer:

Step-by-step explanation:

A vector in R^3 which is not in the span of the set S {(1,2,-2) and (2,-1,1)

If a vector is in the span it can be represented as a linear combination of these two vectors

Let S1 = (1,2,-2) and S2 = (2,-1,1)

i.e. any vector which is of the form

$\alpha S1+\beta S2\\=(\alpha +2\beta,2\alpha -\beta,-2\alpha +\beta)$

Where alpha and beta are any real numbers

Any vector not in this form will not be in the span

i.e. say if alpha = beta =1,

then spanned vector = (3,1,-1)

If we change one coordinate alone say

(3,0,-1) this cannot be represented as a linear combination hence this would be the answer.

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The equation y = \large 1\frac{1}{2}x represents the number of cups of dried fruit, y, needed to make x pounds of granola. Deter

Natasha2012 [34]

Answer:

$(1\frac{1}{2},1)$ - False

$(4,6)$ - True

$(18,12)$ -- False

$(0,0)$ -- True

$(2\frac{1}{2},3\frac{3}{4})$ -- True

Step-by-step explanation:

The points are

$(1\frac{1}{2},1)$ , $(4,6)$ , $(18,12)$ , $(0,0)$ and $(2\frac{1}{2},3\frac{3}{4})$ ---- missing from the question

Given

$y = 1\frac{1}{2}x$

Required

Determine if each of the points would be on $y = 1\frac{1}{2}x$

To do this, we simply substitute the value of x and of each point in $y = 1\frac{1}{2}x$ .

(a) $(1\frac{1}{2},1)$

In this case;

$x = 1\frac{1}{2}$ and $y = 1$

$y = 1\frac{1}{2}x$ becomes

$y = 1\frac{1}{2} * 1\frac{1}{2}$

$y = \frac{3}{2} * \frac{3}{2}$

$y = \frac{9}{4}$

$y = 2\frac{1}{4}$

The point $(1\frac{1}{2},1)$ won't be on the graph because the corresponding value of y for $x = 1\frac{1}{2}$ is $y = 2\frac{1}{4}$

(b) $(4,6)$

In this case;

$x = 4$

$y = 6$

$y = 1\frac{1}{2}x$ becomes

$y = 1\frac{1}{2} * 4$

$y = \frac{3}{2} * 4$

$y = \frac{3* 4}{2}$

$y = \frac{12}{2}$

$y = 6$

The point $(4,6)$ would be on the graph because the corresponding value of y for $x = 4$ is $y = 6$

(c) $(18,12)$

In this case:

$x = 18;y = 12$

$y = 1\frac{1}{2}x$ becomes

$y = 1\frac{1}{2} * 18$

$y = \frac{3}{2} * 18$

$y = \frac{3* 18}{2}$

$y = \frac{54}{2}$

$y = 27$

The point $(18,12)$ wouldn't be on the graph because the corresponding value of y for $x = 18$ is $y = 12$

(d) $(0,0)$

In this case;

$x =0; y = 0$

$y = 1\frac{1}{2}x$ becomes

$y = 1\frac{1}{2} * 0$

$y = 0$

The point $(0,0)$ would be on the graph because the corresponding value of y for $x = 0$ is $y = 0$

(e) $(2\frac{1}{2},3\frac{3}{4})$

In this case:

$x = 2\frac{1}{2}$ ; $y = 3\frac{3}{4}$

$y = 1\frac{1}{2}x$ becomes

$y = 1\frac{1}{2} * 2\frac{1}{2}$

$y = \frac{3}{2} * \frac{5}{2}$

$y = \frac{15}{4}$

$y = 3\frac{3}{4}$

The point $(2\frac{1}{2},3\frac{3}{4})$ would be on the graph because the corresponding value of y for $x = 2\frac{1}{2}$ is $y = 3\frac{3}{4}$

3 0

2 years ago

29. Find CD. 30. Find ZV.

Tems11 [23]

Answer:

for cd it's 12 I believe fs

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2 years ago

Find the earnings rounded to the nearest cent sales: $984 commission: 10%

Scilla [17]

Answer:

$1082

Step-by-step explanation:

10% of $984

10/100 ($984)= $98.4

Earnings = ($98.4+$984)

Earnings = $1082.4

Earnings = $1082 (to the nearest cent)

6 0

3 years ago

Please help me with my math homework what is the answer!!!

Dmitry [639]

Answer:

Step-by-step explanation:

The letters are easy enough.

y^3 determines that 3 ys are needed. y^2 is taken in by the cubed.

x^4 determines that 4 xs are needed. x^3 is part of x^4 and you don't need any more xs

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12: 2 * 2 * 3

42: 2 * 3 * 7

You need two 2s.

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2 years ago

Write an expression equal to 11³

NikAS [45]

Answer:

11x11x11=11³

Step-by-step explanation:

11 to the third means 11 times itself 3 times

3 0

2 years ago

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