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1 Problem 10: Consider the matrix B= 0 -2 1 (4) Find a basis for the null space of B. (5) Verify that Rank (B) + Null(B) : = 318 1 (1) Find a basis for the row space of B. (2) Find a basis for the column space of B. (3) Verify that the row space of B and the column space of B have the same dimension. Number of columns of B.

1 Problem 10: Consider the matrix B= 0 -2 1 (4) Find a basis for the null space of B. (5) Verify that Rank (B) + Null(B) : = 318 1 (1) Find a basis for the row space of B. (2) Find a basis for the column space of B. (3) Verify that the row space of B and the column space of B have the same dimension. Number of columns of B.

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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Problem 10: Consider the matrix B = 1 0 1 3 -1 ܘ 0 (1) Find a basis for the row space of B. (2) Find a basis for the column space of B. (3) Verify that the row space of B and the column space of B have the same dimension. (4) Find a basis for the null space of B. (5) Verify that Rank (B) + Null(B) = Number of columns of B.
Transcribed Image Text:Problem 10: Consider the matrix B = 1 0 1 3 -1 ܘ 0 (1) Find a basis for the row space of B. (2) Find a basis for the column space of B. (3) Verify that the row space of B and the column space of B have the same dimension. (4) Find a basis for the null space of B. (5) Verify that Rank (B) + Null(B) = Number of columns of B.
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