29 213X1X2-H027. Let 9₁, 92, 93, and v represent vectors in R5, and let x₁, x2,and x3 denote scalars. Write the following vector equation asa matrix equation. Identify any symbols you choose to use.X19₁ + x₂9₂ + X3q3 = V28. Rewrite the (numerical) matrix equation below in symbolicform as a vector equation, using symbols V₁, V2,... for thevectors and C₁, C2, ... for scalars. Define what each symbolrepresents, using the data given in the matrix equation.SG71-3 5 -4 9 7581 -2 -4-3724-128-[-]29. Construct a 3 x 3 matrix, not in echelon form, whosecolumns span R³. Show that the matrix you construct has thedesired property.30. Construct a 3 x 3 matrix, not in echelon form, whosecolumns do not span R³. Show that the matrix you constructhas the desired property.31. Let A be a 3 x 2 matrix. Explain why the equation Ax = bcannot be consistent for all b in R³. Generalize yourMastering Linear Algebra Concepts: Span 1-181. The matrix equation[M] Inspan R37.39.beСО40.41. [142. LWESOLUTIONS TO PRACTICE I1

Answered: Construct a 3 x 3 matrix, not in…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

2
1
3
X1
X2
-H
0
27. Let 9₁, 92, 93, and v represent vectors in R5, and let x₁, x2,
and x3 denote scalars. Write the following vector equation as
a matrix equation. Identify any symbols you choose to use.
X19₁ + x₂9₂ + X3q3 = V
28. Rewrite the (numerical) matrix equation below in symbolic
form as a vector equation, using symbols V₁, V2,... for the
vectors and C₁, C2, ... for scalars. Define what each symbol
represents, using the data given in the matrix equation.
SG
71
-3 5 -4 9 7
581 -2 -4
-37
2
4
-1
2
8
-[-]
29. Construct a 3 x 3 matrix, not in echelon form, whose
columns span R³. Show that the matrix you construct has the
desired property.
30. Construct a 3 x 3 matrix, not in echelon form, whose
columns do not span R³. Show that the matrix you construct
has the desired property.
31. Let A be a 3 x 2 matrix. Explain why the equation Ax = b
cannot be consistent for all b in R³. Generalize your
Mastering Linear Algebra Concepts: Span 1-18
1. The matrix equation
[M] In
span R
37.
39.
be
СО
40.
41. [
1
42. L
WE
SOLUTIONS TO PRACTICE I
1

Expert Solution

Step 1

Here's one example of a 3x3 matrix whose span is R^3:

1 2 3
4 5 6
7 8 9

To show that this matrix has the desired property, we need to demonstrate that the set of all linear combinations of its columns forms the entire 3-dimensional space. This can be done by showing that the columns are linearly independent and that they span the space.

Linear independence: The columns of the matrix are linearly independent, meaning that no column can be expressed as a linear combination of the others. For example, the first column (1, 4, 7) cannot be expressed as a combination of the second and third columns (2, 5, 8) and (3, 6, 9).

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