Please help. This problem involves vector subspaces. One picture includes sets 11-13 and the other includes sets 14-15. In Exercises 11 – 15 which of the sets S are subspaces?11. S = {(a,b, c) E R³ : a> 0, b > 0, c> 0}.{(x1, x2, x3) E R°0 where a1, a2, a3 E R are fixed}.12. S =a1x1 + a2x2 + a3x3:R²{(x, y)(x, y) is on the line through (1, 1) with slope 1}.13.S: 14. S= {x E R' : Ax = 0} where A is a 3 × 2 matrix.15. S{x € R : Ax = b} where A is a 3 x 2 matrix and3bE R° is a fixed nonzero vector.

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In Exercises 11 – 15 which of the sets S are subspaces? 11. S= {(a, b, c) E R° : a > 0, b > 0, c > 0}. {(x1, x2, x3) E R° 0 where a1, a2, a3 E R are fixed}. 12. S = a1x1 + a2x2 + a3x3 : R² {(x, y) (x, y) is on the line through (1, 1) with slope 1}. 13. S :

In Exercises 11 – 15 which of the sets S are subspaces? 11. S= {(a, b, c) E R° : a > 0, b > 0, c > 0}. {(x1, x2, x3) E R° 0 where a1, a2, a3 E R are fixed}. 12. S = a1x1 + a2x2 + a3x3 : R² {(x, y) (x, y) is on the line through (1, 1) with slope 1}. 13. S :

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 37EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the...

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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Please help. This problem involves vector subspaces. One picture includes sets 11-13 and the other includes sets 14-15.

In Exercises 11 – 15 which of the sets S are subspaces?
11. S = {(a,b, c) E R³ : a
> 0, b > 0, c> 0}.
{(x1, x2, x3) E R°
0 where a1, a2, a3 E R are fixed}.
12. S =
a1x1 + a2x2 + a3x3
:
R²
{(x, y)
(x, y) is on the line through (1, 1) with slope 1}.
13.
S
:

14. S= {x E R' : Ax = 0} where A is a 3 × 2 matrix.
15. S
{x € R : Ax = b} where A is a 3 x 2 matrix and
3
bE R° is a fixed nonzero vector.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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