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1 1 3 1 2 -1 0 1 -1 1 3. Consider the matrix A = -3 2 1 -2 4 1 6 1 i. Find the row space, R(A), and column space C(A) of A in terms of linearly independent rows and columns of A, respectively. ii. Find the bases for R(A) and C(A) in 2 (i) iii. Find dim (R(A)) and dim (C(A)) iv. Find the rank (A) V. Find the basis and dimension of N(A) (N(A) is the solution space of the homogeneous system Ax = 0 ) vi. If the system Ax = b is consistent where b = , find the complete solution in the form x = xp+Xpwhere xp denotes a particular solution and xp denotes a solution of the associated nonhomogeneous system Ax = 0.

1 1 3 1 2 -1 0 1 -1 1 3. Consider the matrix A = -3 2 1 -2 4 1 6 1 i. Find the row space, R(A), and column space C(A) of A in terms of linearly independent rows and columns of A, respectively. ii. Find the bases for R(A) and C(A) in 2 (i) iii. Find dim (R(A)) and dim (C(A)) iv. Find the rank (A) V. Find the basis and dimension of N(A) (N(A) is the solution space of the homogeneous system Ax = 0 ) vi. If the system Ax = b is consistent where b = , find the complete solution in the form x = xp+Xpwhere xp denotes a particular solution and xp denotes a solution of the associated nonhomogeneous system Ax = 0.

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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Please answer all the questions correctly and briefly. It's all under the same question. Please answer every question especially v, vi.

1 1 3 1 2 -3 -1 2 1 -2 -1 3. Consider the matrix A 4 1 1 i. Find the row space, R(A), and column space C(A) of A in terms of linearly independent rows and columns of A, respectively. ii. Find the bases for R(A) and C(A) in 2 (i) 111. Find dim (R(A)) and dim (C(A)) iv. Find the rank (A) Find the basis and dimension of N(A) (N(A) is the solution space of the V. homogeneous system Ax = 0) vi. If the system Ax = b is consistent where b = find the complete solution in the form x = x,+xpwhere x, denotes a particular solution and xp denotes a solution of the associated nonhomogeneous system Ax = 0.
Transcribed Image Text:1 1 3 1 2 -3 -1 2 1 -2 -1 3. Consider the matrix A 4 1 1 i. Find the row space, R(A), and column space C(A) of A in terms of linearly independent rows and columns of A, respectively. ii. Find the bases for R(A) and C(A) in 2 (i) 111. Find dim (R(A)) and dim (C(A)) iv. Find the rank (A) Find the basis and dimension of N(A) (N(A) is the solution space of the V. homogeneous system Ax = 0) vi. If the system Ax = b is consistent where b = find the complete solution in the form x = x,+xpwhere x, denotes a particular solution and xp denotes a solution of the associated nonhomogeneous system Ax = 0.
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