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3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

Advanced Engineering Mathematics
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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1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1, 8), (7, 2, 3)}? Give the dimension of the subspace spanned by the vectors. 2. Determine all real numbers x € R for which the vectors (x, 0, 1), (2, x, 3), and (4, 5, 6) are linearly independent. 3. Find the set of vectors in R³ which are orthogonal to both (4, 2,0) and (3, 6, 9). 4. Use properties of matrix algebra (Notes 8) to help evaluate the following: -2 [o 3 (a) 7 (b) 5. Use a sequence of elementary row operations to calculate the inverse of the following matrix: ГО 1 01 A = 1 2 3 2 0 1 6. Using the previous result, solve the system of equations 2x + z = 2 y = 8 x + 2y + 3z = 4
Transcribed Image Text:1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1, 8), (7, 2, 3)}? Give the dimension of the subspace spanned by the vectors. 2. Determine all real numbers x € R for which the vectors (x, 0, 1), (2, x, 3), and (4, 5, 6) are linearly independent. 3. Find the set of vectors in R³ which are orthogonal to both (4, 2,0) and (3, 6, 9). 4. Use properties of matrix algebra (Notes 8) to help evaluate the following: -2 [o 3 (a) 7 (b) 5. Use a sequence of elementary row operations to calculate the inverse of the following matrix: ГО 1 01 A = 1 2 3 2 0 1 6. Using the previous result, solve the system of equations 2x + z = 2 y = 8 x + 2y + 3z = 4
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