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Chapter 6: Q64E (page 277)

In Exercises 62 through 64, consider a function from to that is linear in both columns and alternating on the columns. See Examples 4 and 6 and the subsequent discussions. Assume that .


64. Using Exercises 62 and 63 as a guide, show that D(A)=ad-bc=detAfor all 2脳2matrices A .

Short Answer

Expert verified

Dabcd=ad-bc

Step by step solution

01

Matrix Definition

Matrix is aset of numbersarranged in 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 an 鈥� m by n 鈥� matrix, written 鈥� m脳n.鈥�

02

To show that D(A) = ad - bc= detA 

To show:

D(A)=ad-bc=detA

To solve,

Take L.H.S:

DabcdDabcd=Dabcd+D0bcdDabcd=Dab0d-cd0bDabcd=ad-bc

Therefore,

L.H.S R.H.S

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Most popular questions from this chapter

For an invertiblenxnmatrix A, what is the relationship betweenadj(A)andadj(A-1) a?

IfA is an n脳n matrix of rank n-1, what is the rank of adj(A)? See Exercises 42 and 43.

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24.T(z)=(2+3i)zfrom鈩�to鈩�

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