Which of the followings describe all the solutions to the equation: x1 + 2x2 + 4x3 = 2? %3D 1. {(2, 0, 0)} 2. {(2 – 4t, 2s, t – 8)|t, s E R} 3. {t(4, 0, –1) + s(-4, 0,1) + (0, 1, 0)|s, t e R} 4. {(2t + 2, -t, t)|t e R} 5. {(2 – 2x2 – 4x3, x2, x3)|x2, x3 E R} 6. {(x1, x2 + 1, x3)|(x1, x2, x3) statisfies x1 + 2x2 + 4x3 = 0} Please type the numbers without empty spaces to the blank. For example, 12 stands for only the first two sets describe all the solutions. 15 Suppose A is a 4 × 5 matrix. For any b E R*, Ax = b is consistent. 4 Then the number of pivots of A is and the number of solutions for Ax = b is infinity
Which of the followings describe all the solutions to the equation: x1 + 2x2 + 4x3 = 2? %3D 1. {(2, 0, 0)} 2. {(2 – 4t, 2s, t – 8)|t, s E R} 3. {t(4, 0, –1) + s(-4, 0,1) + (0, 1, 0)|s, t e R} 4. {(2t + 2, -t, t)|t e R} 5. {(2 – 2x2 – 4x3, x2, x3)|x2, x3 E R} 6. {(x1, x2 + 1, x3)|(x1, x2, x3) statisfies x1 + 2x2 + 4x3 = 0} Please type the numbers without empty spaces to the blank. For example, 12 stands for only the first two sets describe all the solutions. 15 Suppose A is a 4 × 5 matrix. For any b E R*, Ax = b is consistent. 4 Then the number of pivots of A is and the number of solutions for Ax = b is infinity
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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Answer all parts of the question
Transcribed Image Text:Which of the followings describe all the solutions to the equation: x1 + 2x2 + 4x3 = 2 ?
1. {(2, 0, 0)}
2. {(2 – 4t, 2s, t – s)\t, s e R}
-
3. {t(4,0, –1) + s(-4,0, 1) + (0, 1, 0)|s, t E R}
4. {(2t + 2, –t, t)|t e IR}
5. {(2 – 2x2 – 4x3, x2, x3)|x2, x3 ER}
6. {(x1, x2 + 1, x3)|(x1, x2, x3) statisfies x1 + 2x2 + 4x3 = 0}
Please type the numbers without empty spaces to the blank.
For example, 12 stands for only the first two sets describe all the solutions.
15
Suppose A is a 4 × 5 matrix. For any b E R*, A = b is consistent.
Then the number of pivots of A is 4
and the number of solutions for A = 6 is infinity
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