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Suppose aj, az, az, a, and a, are vectors in R, and they are, in order from left to right, the five columns of the matrix (A), so that A = [aj | az | a | a, | as), and 3 4 rref (A) = 0 1 0 lo 0 1 -3 1 a. Select all of the true statements (there may be more than one correct answer). OA. {āj, az} is a linearly independent set OB. {aj, az, ag, as} is a basis for R³ OC. {ãj, ã2, ã3} is a linearly independent set OD. {ãi, a2, ā3, a4} is a linearly independent set OE. span(ai, a2, az) = R³ OF. span(aj, az) = R³ OG. {aj, a, ä} is a basis for R OH. {ãj, az} is a basis for R3 Ol. span(ai, a2, az, ãs) = R³ b. If possible, write a, as a linear combination of aj, az, and az; otherwise, enter "DNE". You may enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". c. The dimension of the image of A is and the image of A is a subspace of (enter "RAn" with a specfic number for "n"). d. Find a basis for the image of A. Enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Enter your answer as a comma separated list of vectors. A basis for the image of A is { e. The dimension of the kernel of A is and the kernel of A is a subspace of (enter "R^n" with a specfic number for "n"). f. If ëj = (-3, 3, –1,1,0), then Aæi = Enter "a1" for āj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Is xi in the kernel of A? choose v g. If 2 = (-4, –2, –2, 0, 1), then A2 = . Is x2 in the kernel of A? choose v h. If ag = 32 - 4x = then Axg = . Is x3 in the kernel of A? choose v i. Find a basis for the kernel of A. Enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4>". Enter your answer as a comma separated list of vectors.

Suppose aj, az, az, a, and a, are vectors in R, and they are, in order from left to right, the five columns of the matrix (A), so that A = [aj | az | a | a, | as), and 3 4 rref (A) = 0 1 0 lo 0 1 -3 1 a. Select all of the true statements (there may be more than one correct answer). OA. {āj, az} is a linearly independent set OB. {aj, az, ag, as} is a basis for R³ OC. {ãj, ã2, ã3} is a linearly independent set OD. {ãi, a2, ā3, a4} is a linearly independent set OE. span(ai, a2, az) = R³ OF. span(aj, az) = R³ OG. {aj, a, ä} is a basis for R OH. {ãj, az} is a basis for R3 Ol. span(ai, a2, az, ãs) = R³ b. If possible, write a, as a linear combination of aj, az, and az; otherwise, enter "DNE". You may enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". c. The dimension of the image of A is and the image of A is a subspace of (enter "RAn" with a specfic number for "n"). d. Find a basis for the image of A. Enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Enter your answer as a comma separated list of vectors. A basis for the image of A is { e. The dimension of the kernel of A is and the kernel of A is a subspace of (enter "R^n" with a specfic number for "n"). f. If ëj = (-3, 3, –1,1,0), then Aæi = Enter "a1" for āj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Is xi in the kernel of A? choose v g. If 2 = (-4, –2, –2, 0, 1), then A2 = . Is x2 in the kernel of A? choose v h. If ag = 32 - 4x = then Axg = . Is x3 in the kernel of A? choose v i. Find a basis for the kernel of A. Enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4>". Enter your answer as a comma separated list of vectors.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Suppose aj, az, az, ag, and a, are vectors in R, and they are, in order from left to right, the five columns of the matrix (A), so that A = [ai| az | az | as | aj), and [1 0 0 rref(A) = 0 1 0 -3 2 0 0 1 1 41 2 a. Select all of the true statements (there may be more than one correct answer). OA. {ãi, a2} is a linearly independent set OB. {ai, a2, a3, a4} is a basis for R³ OC. {āj, a2, āz} is a linearly independent set OD. {ãi, a2, ā3, a4} is a linearly independent set OE. span(ãi, ā2, āz) = R³ OF. span(ai, az) = R³ OG. {aj, a2, āz} is a basis for R3 OH. {ãi, a2} is a basis for R OI. span(aj, a2, a3, a4) = R3 b. If possible, write a, as a linear combination of aj, az, and az; otherwise, enter "DNE". You may enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4,5>". c. The dimension of the image of A is , and the image of A is a subspace of (enter "RAn" with a specfic number for "n"). d. Find a basis for the image of A. Enter “a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Enter your answer as a comma separated list of vectors. A basis for the image of A is { | } e. The dimension of the kernel of A is ,and the kernel of A is a subspace of (enter "R^n" with a specfic number for "n"). f. If z = (-3,3, –1,1,0), then Aãi = Enter "a1" for āj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Is xi in the kernel of A? choose v g. If 2 = (-4, –2, –2,0, 1), then Aa2 = Is x2 in the kernel of A? choose v h. If az = 32 – 4 = , then Ax3 = . Is x3 in the kernel of A? choose v i. Find a basis for the kernel of A. Enter "a1" for ãi, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4>". Enter your answer as a comma separated list of vectors. A basis for the kernel of A is {
Transcribed Image Text:Suppose aj, az, az, ag, and a, are vectors in R, and they are, in order from left to right, the five columns of the matrix (A), so that A = [ai| az | az | as | aj), and [1 0 0 rref(A) = 0 1 0 -3 2 0 0 1 1 41 2 a. Select all of the true statements (there may be more than one correct answer). OA. {ãi, a2} is a linearly independent set OB. {ai, a2, a3, a4} is a basis for R³ OC. {āj, a2, āz} is a linearly independent set OD. {ãi, a2, ā3, a4} is a linearly independent set OE. span(ãi, ā2, āz) = R³ OF. span(ai, az) = R³ OG. {aj, a2, āz} is a basis for R3 OH. {ãi, a2} is a basis for R OI. span(aj, a2, a3, a4) = R3 b. If possible, write a, as a linear combination of aj, az, and az; otherwise, enter "DNE". You may enter "a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4,5>". c. The dimension of the image of A is , and the image of A is a subspace of (enter "RAn" with a specfic number for "n"). d. Find a basis for the image of A. Enter “a1" for aj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Enter your answer as a comma separated list of vectors. A basis for the image of A is { | } e. The dimension of the kernel of A is ,and the kernel of A is a subspace of (enter "R^n" with a specfic number for "n"). f. If z = (-3,3, –1,1,0), then Aãi = Enter "a1" for āj, etc., or enter coordinate vectors of the form "<1,2,3>" or " <1,2,3,4,5>". Is xi in the kernel of A? choose v g. If 2 = (-4, –2, –2,0, 1), then Aa2 = Is x2 in the kernel of A? choose v h. If az = 32 – 4 = , then Ax3 = . Is x3 in the kernel of A? choose v i. Find a basis for the kernel of A. Enter "a1" for ãi, etc., or enter coordinate vectors of the form "<1,2,3>" or "<1,2,3,4>". Enter your answer as a comma separated list of vectors. A basis for the kernel of A is {
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