Problem 5. Mark the statements as true or false:(a) Let A be an invertible 3 × 3 matrix. Then all the columns of A are pivot columns.(b) Let A be a 4 x 4 matrix and it has a pivot position in every row. Then Det(A) = 0 .(c) Let A be an n × n matrix and the linear system A = b has a unique solution for all vectorsb is R". Then Det(A) # 0.(d) Let A be a 3 x 3 matrix and Nul A has only the trivial solution. Then Det (A) + 0.(e) Let A be a 4 x 4 matrix such that Rank(A) = 3. Then Det(A) = 0.

As per rule, we will solve first three subparts: Q.5 1) Let A be 3×3 invertible matrix.…

Problem 5. Mark the statements as true or false: (a) Let A be an invertible 3 x 3 matrix. Then all the columns of A are pivot columns. (b) Let A be a 4 x 4 matrix and it has a pivot position in every row. Then Det(A) = 0 . (c) Let A be an n x n matrix and the linear system A = b has a unique solution for all vectors b is R". Then Det(A) # 0.

Problem 5. Mark the statements as true or false: (a) Let A be an invertible 3 x 3 matrix. Then all the columns of A are pivot columns. (b) Let A be a 4 x 4 matrix and it has a pivot position in every row. Then Det(A) = 0 . (c) Let A be an n x n matrix and the linear system A = b has a unique solution for all vectors b is R". Then Det(A) # 0.

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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Question

Problem 5. Mark the statements as true or false:
(a) Let A be an invertible 3 × 3 matrix. Then all the columns of A are pivot columns.
(b) Let A be a 4 x 4 matrix and it has a pivot position in every row. Then Det(A) = 0 .
(c) Let A be an n × n matrix and the linear system A = b has a unique solution for all vectors
b is R". Then Det(A) # 0.
(d) Let A be a 3 x 3 matrix and Nul A has only the trivial solution. Then Det (A) + 0.
(e) Let A be a 4 x 4 matrix such that Rank(A) = 3. Then Det(A) = 0.

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