Consider the statements:i)The rank of a matrix is the maximum number of linearly independent columnsin the matrix.ii)If the rank of an nxn matrix is n, then it is non-singular.a) Both (i) and (ii) are false.b) Both (i) and (ii) are true.c) (i) is true but (ii) is falsed) (i) is false and (ii) is true.

To find the rank of a matrix find its order first and then check how many columns are linear…

Consider the statements: i) The rank of a matrix is the maximum number of linearly independent columns in the matrix. ii) If the rank of an n×n matrix is n, then it is non-singular. a) Both (i) and (ii) are false. b) Both (i) and (ii) are true. c) (i) is true but (ii) is false d) (i) is false and (ii) is true.

Consider the statements: i) The rank of a matrix is the maximum number of linearly independent columns in the matrix. ii) If the rank of an n×n matrix is n, then it is non-singular. a) Both (i) and (ii) are false. b) Both (i) and (ii) are true. c) (i) is true but (ii) is false d) (i) is false and (ii) is true.

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Consider the statements:
i)
The rank of a matrix is the maximum number of linearly independent columns
in the matrix.
ii)
If the rank of an nxn matrix is n, then it is non-singular.
a) Both (i) and (ii) are false.
b) Both (i) and (ii) are true.
c) (i) is true but (ii) is false
d) (i) is false and (ii) is true.

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