(a) Let C₁, C2, C3, and ♬ be the columns given below. Let C be the matrix C = [ ₁ ₂ 3 ]. That is, C is the matrix with columns C₁, C2, and c3, in that order. = 1 2 " = 2 C3 = 0 > a -8 S = b Compute the product Cs, and show that it is equal to the linear combination of c₁, c2, and 3 with coefficients a, b, and c. (b) Let d = 7c₁ +872 +973. Show that the system C = d is consistent. (Hint: Use the result of part (a). You don't have to row reduce anything here!) (c) Conclude from the ideas in the previous two parts that the system of equations Cx = has a solution if and only if b is equal to a linear combination of 1, 2, 3 (the columns of C).
(a) Let C₁, C2, C3, and ♬ be the columns given below. Let C be the matrix C = [ ₁ ₂ 3 ]. That is, C is the matrix with columns C₁, C2, and c3, in that order. = 1 2 " = 2 C3 = 0 > a -8 S = b Compute the product Cs, and show that it is equal to the linear combination of c₁, c2, and 3 with coefficients a, b, and c. (b) Let d = 7c₁ +872 +973. Show that the system C = d is consistent. (Hint: Use the result of part (a). You don't have to row reduce anything here!) (c) Conclude from the ideas in the previous two parts that the system of equations Cx = has a solution if and only if b is equal to a linear combination of 1, 2, 3 (the columns of C).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(a) Let č₁, C2, C3, and s' be the columns given below. Let C be the matrix C = [ ₁ ₂ 3 ]. That is, C is
the matrix with columns č₁, №2, and №3, in that order.
--8-8-8-8
2
2
3
0
= =
a
b
Compute the product Cs, and show that it is equal to the linear combination of c₁, c2, and 3 with
coefficients a, b, and c.
(b) Let đ= 7c₁ +872 +973. Show that the system C = d is consistent.
(Hint: Use the result of part (a). You don't have to row reduce anything here!)
(c) Conclude from the ideas in the previous two parts that the system of equations Cỡ = b has a solution
if and only if b is equal to a linear combination of c₁, C2, C3 (the columns of C).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc84b9504-04d8-4492-b13a-660d2a574b53%2F83234300-77f3-4315-9b5f-ea98ab7ded79%2Fy3lp34r_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let č₁, C2, C3, and s' be the columns given below. Let C be the matrix C = [ ₁ ₂ 3 ]. That is, C is
the matrix with columns č₁, №2, and №3, in that order.
--8-8-8-8
2
2
3
0
= =
a
b
Compute the product Cs, and show that it is equal to the linear combination of c₁, c2, and 3 with
coefficients a, b, and c.
(b) Let đ= 7c₁ +872 +973. Show that the system C = d is consistent.
(Hint: Use the result of part (a). You don't have to row reduce anything here!)
(c) Conclude from the ideas in the previous two parts that the system of equations Cỡ = b has a solution
if and only if b is equal to a linear combination of c₁, C2, C3 (the columns of C).
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