Description
its about Linear Algebra assignment please see the file that I attached to see the questions thanks.
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Explanation & Answer
please find the attachmentsI have uploaded answers in both word and PDF formatIt is better if you use PDF formatbecause when using word format some features may changed based on your version.
Exercises:
1) a) X1 + 5X 2 − (√2)X 3 = 1
𝑏) X1 = −7X 2 + 3X 3
𝑐) πX1 − √2X 2 = 72
d) X1 + 3X2 + X1 X3 = 2
This equation is not a linear equation. Because it has a term of multiplication of two variables.
e) X1 −2 + X 2 + 8X 3 = 5
This equation is not a linear equation. Because it has an exponential term ( X1 −2).
2)
𝑥 − 𝑦 + 2𝑧 − 𝑤 = −1
2𝑥 + 𝑦 − 2𝑧 − 𝑤 = −2
−𝑥 + 2𝑦 − 4𝑧 + 𝑤 = 1
3𝑥
− 3𝑤 = −3
Re writing in matrix form
1 −1 2 −1 −1
2 1 −2 −1 −2
(
| )
−1 2 −4 1 1
3 0 0 −3 −3
Recognize the pivot of the 1st column in first row
1 −1 2 −1 −1
2 1 −2 −1 −2
(
| )
−1 2 −4 1 1
3 0 0 −3 −3
...