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Chapter 6: Q8E (page 306)

Demonstrate the equation |detA|=||v鈫�1||||v鈫�12||....||v鈫�n鈯�||for a noninvertiblen脳nmatrixA=[v鈫�1v鈫�1.........v鈫�n](Theorem 6.3.3).

Short Answer

Expert verified

Since the columns of A are linearly dependent, this means that 鈭�i鈭�1,.....,n,v鈫�i鈯�=0.

So the right side of this equation is also 0.

Step by step solution

01

Matrix Definition. 

Matrix is aset of numbers arrangedin rows and columns soas to form a rectangulararray.

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� by 鈥� matrix, written 鈥渕 x n .鈥�

02

To demonstrate the equation. 

If

A=v鈫�1v鈫�1......v鈫�n鈭�鈩�n脳n

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

Since the columns of are linearly dependent, this means that鈭�i鈭�1,....,nv鈫�i鈯�=0.

So the right side of this equation is also 0.

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