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Chapter 6: Q29E (page 309)

29. IfA=u鈫�v鈫�w鈫�is a3脳3 matrix, then the formuladetA=V鈫�.u鈫�脳w鈫� must hold.

Short Answer

Expert verified

Therefore, the given statement is True.

Step by step solution

01

Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as 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 check whether the given condition is true or false.

Let,

For example,

A=l3,

then

u=e1,v=e2,w=e3,

Now,

v.u脳w=e2.e1脳e3v.u脳w=e2.-e2v.u脳w=-1v.u脳w鈮�1v.u脳w=detA

Therefore, the given statement is True.

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Most popular questions from this chapter

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

positive or negative? How can you tell? Do not use technology.

There exist real invertible 3脳3 matrices A and S such that .

Find the determinants of the linear transformations in Exercises 17 through 28.

18.T(f)=2f+3f'fromP2toP2

Question:A basisv1鈫�,v2鈫�,v3鈫�of鈩�3is called positively oriented ifv1鈫�encloses an acute angle withv2鈫�脳v3鈫�. Illustrate this definition with a sketch. Show that the basis is positively oriented if (and only if)det[v1鈫�,v2鈫�,v3鈫�]is positive.

If A and Bare invertible n脳nmatrices, and if Ais similar toB, isadj(A) necessarily similar to adj(B)?
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