
Concept explainers
Any 2 by 3 matrix of rank one, set the

Answer to Problem 1PS
The matrix A of order 2 by 3 be
Explanation of Solution
Given:
Let the matrix A of order 2 by 3 be
Hence, Rank of A is 1, which is equals to the dimension of row space.
From the figure, dimension of row space is r =1,
From rank-nullity theorem, dimension of null space of A is
Since row space spanned by (1, 2, 3), now we have to choose null space such that their dot product with (1, 2, 3) is zero. Which is the condition for orthogonal.
So, null space
Now the similar way if we look at the dimension of column space of A is also 1, because the rank of ATis also 1.
Which implies, Null space of ATis
We choose null space of ATis (2,-1). Since the column space vector is orthogonal (2,-1).
Now, Let us set a figure with above information.
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Chapter 4 Solutions
Introduction to Linear Algebra, Fifth Edition
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