Linear Algebra. Determine if b is a linear combination of the vectors formed from the columns of the matrix A.1- 4- 412A =46.b =- 74 - 16156.Choose the correct answer below.O A. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution to the linear system corresponding to the matrix[Ab]B. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in thefirst column and the second entry in the second column. There are no pivots in the third and fourth columns.C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in thefirst column, the second entry in the second column, and the third entry in the third column.D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are only in the firstentry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns. 1- 6Let a, =3- 13and b =For what value(s) of h is b in the plane spanned by a, and a,?13The value(s) of h is(are)(Use a comma to separate answers as needed.)

A=1-4-40464-1615 , b=12-76Let A= a1a2a3and x1a1+x2a2+x3a3=bTher augmented matrix…

Answered: Determine if b is a linear combination…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...

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Linear Algebra.

Determine if b is a linear combination of the vectors formed from the columns of the matrix A.
1
- 4
- 4
12
A =
4
6.
b =
- 7
4 - 16
15
6.
Choose the correct answer below.
O A. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution to the linear system corresponding to the matrix
[Ab]
B. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the
first column and the second entry in the second column. There are no pivots in the third and fourth columns.
C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the
first column, the second entry in the second column, and the third entry in the third column.
D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are only in the first
entry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns.

1
- 6
Let a, =
3
- 13
and b =
For what value(s) of h is b in the plane spanned by a, and a,?
1
3
The value(s) of h is(are)
(Use a comma to separate answers as needed.)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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