Linear Algebra Determine if b is a linear combination of a1, a2, and a3.142a, =- 2, a2 =az =- 4- 2416Choose the correct answer below.A. Vector b is a linear combination of a,, a,, and az. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in thesecond column, and the third entry in the third column.B. Vector b is a linear combination of a,, a,, and az. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in thesecond column, and the third entry in the fourth column.O C. Vector b is not a linear combination of a,, a2, and a3.D. Vector b is a linear combination of a,, a,, and az. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry inthe second column. Use the accompanying figure to write each vector listed as a linear combination of u and v.toVectors c, x, y, and z2vW.-2vyWrite c as a linear combination of u and v.Ov(Type integers or decimals.)C =u +V

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

Determine if b is a linear combination of a1, a2, and a3.
1
4
2
a, =
- 2
, a2 =
az =
- 4
- 2
4
16
Choose the correct answer below.
A. Vector b is a linear combination of a,, a,, and az. 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.
B. Vector b is a linear combination of a,, a,, and az. 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 fourth column.
O C. Vector b is not a linear combination of a,, a2, and a3.
D. Vector b is a linear combination of a,, a,, and az. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in
the second column.

Use the accompanying figure to write each vector listed as a linear combination of u and v.
to
Vectors c, x, y, and z
2v
W.
-2v
y
Write c as a linear combination of u and v.
Ov
(Type integers or decimals.)
C =
u +
V

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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