Question

Determine which of the following subsets of R³ are subspaces of R³. Yes 1. {[$x, x - 9, x + 6]^T | $x$ arbitrary number} Yes 2. {[$x, y, z]^T | $9x - 6y = 0$, $2x - 4z = 0$} No 3. {[$x, y, z]^T | $5x + 8y - 7z = 4$} Yes 4. {$[-4x + 7y, -5x - 3y, -8x + 3y]^T$ | $x, y$ arbitrary numbers} No 5. {$[-4x, -5x, -8x]^T$ | $x$ arbitrary number} No 6. {[$x, y, z]^T | $-9x + 6y - 2z = 0$} No 7. {[$x, y, z]^T | $x \ge 0, y \ge 0, z \ge 0$}

          Determine which of the following subsets of R³ are subspaces of R³.
Yes 1. {[$x, x - 9, x + 6]^T | $x$ arbitrary number}
Yes 2. {[$x, y, z]^T | $9x - 6y = 0$, $2x - 4z = 0$}
No 3. {[$x, y, z]^T | $5x + 8y - 7z = 4$}
Yes 4. {$[-4x + 7y, -5x - 3y, -8x + 3y]^T$ | $x, y$ arbitrary numbers}
No 5. {$[-4x, -5x, -8x]^T$ | $x$ arbitrary number}
No 6. {[$x, y, z]^T | $-9x + 6y - 2z = 0$}
No 7. {[$x, y, z]^T | $x \ge 0, y \ge 0, z \ge 0$}

Determine which of the following subsets of R³ are subspaces of R³.
Yes 1. [x, x - 9, x + 6]^T |xarbitrary number
Yes 2. [x, y, z]^T |9x - 6y = 0,2x - 4z = 0No 3. [x, y, z]^T |5x + 8y - 7z = 4Yes 4. [-4x + 7y, -5x - 3y, -8x + 3y]^T | x, y arbitrary numbers
No 5. [-4x, -5x, -8x]^T | x arbitrary number
No 6. [x, y, z]^T |-9x + 6y - 2z = 0No 7. [x, y, z]^T |x ≥ 0, y ≥ 0, z ≥ 0

Added by Mark F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Madhur L

06/14/2023

Step 1

Step 2: Let's go through each subset and check if it satisfies these properties. Show more…

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Determine which of the following subsets of R³ are subspaces of R³. 1. {[x, x9, x+6]T | x arbitrary number} - Yes 2. {[x, y, z]T | 9x - 6y = 0, 2x − 4z = 0} - Yes 3. {[x, y, z] | 5x + 8y = 72 = 4} - No 4. {[-4x + 7y, -5x − 3y, -8x + 3y]T | x, y arbitrary numbers } - Yes 5. {[-4x, -5x, -8x] | x arbitrary number} - No 6. {[x, y, z] | − 9x + 6y – 2z = 0} - Yes 7. {[x, y, z]¹ | x ≥ 0, y ≥ 0, z ≥ 0} - No Determine which of the following subsets of R³ are subspaces of R³. 1. {[x - 9x + 6] | x arbitrary number} - Yes 2. {[xyz | 9x - 6y = 0, 2x - 4z = 0} - Yes 3. {[xy | 5x + 8y - 7z = 4} - No 4. {[-4z + 7y - 5x - 3y - 8x + 3y] | x, y arbitrary numbers} - Yes 5. {[-4x - 5x, -8z] | x arbitrary number} - No 6. {[xy] | -9x + 6y - 2z = 0} - No 7. {[x, y] | x ≥ 0, y ≥ 0, z ≥ 0} - No