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Chapter 6: Q 6.3-8E (page 306)

Question: Demonstrate the equation for a noninvertiblen 脳 nmatrix (Theorem 6.3.3)..

Short Answer

Expert verified

Since the columns of A are linearly dependent, this means that.

So the right side of this equation is also 0.

Step by step solution

01

Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a 鈥渕 by n鈥� matrix, written 鈥� m 脳 n.鈥�

02

To demonstrate the equation. 

If

Is a non-invertible matrix, then det A = 0.

Since the columns of are linearly dependent, this means that .

So the right side of this equation is also 0.

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