1. 1 1 1 01 0 10 0 0 0 0 0 1 1 0 0 Lo o o 0 1 1 X1 X2 X3 X4 X5 X6 1 1. 2 2 2 Problem 3: The 4 x 6 matrix A and its row-reduced echelon form are: A = 0 3 3 3 3 4 4. X1 X2 X3 X4 X5 X6 a. Fill out the following table of properties of the matrix: Dimension of the Dimension of Dimension of Is the transformation Is the transformation Rank Domain of A Codomain of A null space onto? one-to-one? X17 |X2 -X4 b. In parametric form, the solutions to the homogeneous equation AX = 0 are: = X4 X4 (free) |X5 -X6 X6 (free). In the box, write a basis for the null space of matrix A. Call the two vectors in the basis n and n2. Remember! Rows are rows and columns are columns. Note that your two basis vectors just happen to be orthogonal! (This is not always true, but the problem was designed this way.) c. Normalize your two vectors so they form an orthonormal basis u and for the null space N. Divide both vectors by their mutual 2-norm of -1 1 d. The vector ỹ = = ý + z can be written (uniquely) as the sum of a vector ý in the null space of A, and a vector ž orthogonal JDDDDD JDDDDD

1. 1 1 1 01 0 10 0 0 0 0 0 1 1 0 0 Lo o o 0 1 1 X1 X2 X3 X4 X5 X6 1 1. 2 2 2 Problem 3: The 4 x 6 matrix A and its row-reduced echelon form are: A = 0 3 3 3 3 4 4. X1 X2 X3 X4 X5 X6 a. Fill out the following table of properties of the matrix: Dimension of the Dimension of Dimension of Is the transformation Is the transformation Rank Domain of A Codomain of A null space onto? one-to-one? X17 |X2 -X4 b. In parametric form, the solutions to the homogeneous equation AX = 0 are: = X4 X4 (free) |X5 -X6 X6 (free). In the box, write a basis for the null space of matrix A. Call the two vectors in the basis n and n2. Remember! Rows are rows and columns are columns. Note that your two basis vectors just happen to be orthogonal! (This is not always true, but the problem was designed this way.) c. Normalize your two vectors so they form an orthonormal basis u and for the null space N. Divide both vectors by their mutual 2-norm of -1 1 d. The vector ỹ = = ý + z can be written (uniquely) as the sum of a vector ý in the null space of A, and a vector ž orthogonal JDDDDD JDDDDD

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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D, E and F
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please help with question 2a and 2b ONLY NEVER MIND THE OTHER CONTENT
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