EX 7Using the scalar form of the table331-a6A121154- - a-2126+ a2519to determine the dimension and a non-trivial basis of the row space rowsp(A), thecolumn space colsp(A), and the null space N(A) of A.

Step 1: Write the matrix A in scalar form. A = [[1, 3, 5, 6 + a], [2, 3, 4 - a, 2], [1, 1 - a, - 2,…

Answered: Using the scalar form of the table 1 3…

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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Let 4 -1 0 1 7 A = 13 -11 3 -1 -1 1 -3 13 -1 1 -3] Find orthonormal bases of the kernel and image of A. Basis of the kernel:
[1 2 1 01 2 5 1 1 A = 3 7 2 2 -2 [4 9 3 -1 4] i) Find row space R(A) and column space C(A) of A. ii) Find the bases for row space and column space of A obtained in i). iii) Find dim(R(A)) and dim(C(A)). iv) Find the rank(A).
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7
A= 1 2 2 1 3 0 -6 -3 2 -2 0 0 3 1 -1 3
7 -5 9 4 3 3 8. Let A = -1 2 3 1 1 -3 0 1 0 3 -1 7 0 2 (a) Find a basis for the row space of A, and determine the value of n(A). (b) Find a basis for the nullspace of A", and determine the value of r(A").
[3 -3 A =6 9 -9 -5 a. A basis for the row space of A is { vectors, such as , . }. You should be able to explain and justify your answer. Enter a coordinate vector, such as , or a comma separated list of coordinate b. The dimension of the row space of A is because (select all correct answers -- there may be more than one correct answer): OA. Two of the three columns in rref(A) are free variable columns. OB. rref(A) has a pivot in every row. OC. rref(A) is the identity matrix. OD. The basis we found for the row space of A has two vectors. OE. Two of the three rows in rref(A) do not have a pivot. OF. Two of the three rows in rref(A) have pivots. c. The row space of A is a subspace of because choose d. The geometry of the row space of A is choose
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Let Find orthonormal bases of the kernel, row space, and image (column space) of A. (a) Basis of the kernel: (b) Basis of the row space: {[ | | (c) Basis of the image (column space): IT ].[ A = 3 -1 -3 11 do 0 3 1 - 2 |}
A. Find the rank and nullity B. Find a basis for the column space C. Find a basis for the nullspace
9 - - Let 1 3 5 A = -1 5 4 9 2 4 6 10 Which one is a basis for the column space, C(A), of A

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Using the scalar form of the table 1 3 2 3 1 1- - a 1 6 = 6+ a 5 4-a 2 -2 5 12 19 to determine the dimension and a non-trivial basis of the row space rowsp(A), the column space colsp(A), and the null space N(A) of A.