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Consider the following set. S = {(2, 0, 0), (0, 8, 0), (0, 0, −18), (2, 5, −9)} Solve for c1, c2, c3, and c4 in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c1, c2, c3, c4} = {0, 0, 0, 0}.) c1(2, 0, 0) + c2(0, 8, 0) + c3(0, 0, −18)

Consider the following set. S = {(2, 0, 0), (0, 8, 0), (0, 0, −18), (2, 5, −9)} Solve for c1, c2, c3, and c4 in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c1, c2, c3, c4} = {0, 0, 0, 0}.) c1(2, 0, 0) + c2(0, 8, 0) + c3(0, 0, −18)

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.9: Area Problems
Problem 8P
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Consider the following set.
S = {(2, 0, 0), (0, 8, 0), (0, 0, −18), (2, 5, −9)}

Solve for c1, c2, c3, and c4 in the following equation.
If a nontrivial solution exists, state it or state the general solution in terms of the parameter t.
(If only the trivial solution exists, enter the trivial solution {c1, c2, c3, c4} = {0, 0, 0, 0}.)

c1(2, 0, 0) + c2(0, 8, 0) + c3(0, 0, −18) + c4(2, 5, −9) = (0, 0, 0)

 

{c1, c2, c3, c4} =

 
Consider the following set. S= {(2, 0, 0), (0, 8, 0), (0, 0, -18), (2, 5. -9)} Solve for c,, c,, C2, and c, in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c,, C2, Cz, ca) = {0, 0, 0, 0).) (2, 0, 0) + c2(0, 8, 0) + c3(0, 0, -18) + ca(2, 5, -9) = (0, 0, 0) {c1, c2, c3, c4) = -3 -C4 2 44 Determine whether the set S is linearly independent or linearly dependent. linearly independent linearly dependent
Transcribed Image Text:Consider the following set. S= {(2, 0, 0), (0, 8, 0), (0, 0, -18), (2, 5. -9)} Solve for c,, c,, C2, and c, in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c,, C2, Cz, ca) = {0, 0, 0, 0).) (2, 0, 0) + c2(0, 8, 0) + c3(0, 0, -18) + ca(2, 5, -9) = (0, 0, 0) {c1, c2, c3, c4) = -3 -C4 2 44 Determine whether the set S is linearly independent or linearly dependent. linearly independent linearly dependent
Consider the following set. S = {(2, 0, 0), (o, 8, 0), (0, 0, -18), (2, 5, -9)} Solve for c,, c,, C3, and c, in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c,, C2, C3, Ca) = {0, 0, 0, 0}.) c(2, 0, 0) + c2(0, 8, 0) + c3(0, 0, -18) + c4(2, 5, -9) = (0, o, 0) } -t, t Determine whether the set S is linearly independent or linearly dependent. linearly independent linearly dependent
Transcribed Image Text:Consider the following set. S = {(2, 0, 0), (o, 8, 0), (0, 0, -18), (2, 5, -9)} Solve for c,, c,, C3, and c, in the following equation. If a nontrivial solution exists, state it or state the general solution in terms of the parameter t. (If only the trivial solution exists, enter the trivial solution {c,, C2, C3, Ca) = {0, 0, 0, 0}.) c(2, 0, 0) + c2(0, 8, 0) + c3(0, 0, -18) + c4(2, 5, -9) = (0, o, 0) } -t, t Determine whether the set S is linearly independent or linearly dependent. linearly independent linearly dependent
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