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Chapter 2: Q24E (page 108)

TRUE OR FALSE?

There exists a matrix A such that A(1212)=(1111).

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Compute the matrix

The matrix is said to be invertible, if and only if the reduced row echelon form of the matrix has nonzero diagonal elements and for second order matrix, the determinant of the matrix should be nonzero.

02

Apply the application of inverse

Consider the condition.

A1212=1111鈬�A=11111212-1

If the determinant of the matrix is zero, then, this inverse does not exist.

As det1212=0 thus, the inverse does not exist.

Therefore, the matrix does not exist.

The statement is false.

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Most popular questions from this chapter

Question 7: Suppose v1鈫�,v2鈫�,v3鈫�鈰�vm鈫�are arbitrary vectors in Consider the linear transformation from togiven by

T[x1x2鈰�xm]=[x1v1鈫�,x2v2鈫�,x3v3鈫�鈰�xmvm鈫�]

TRUE OR FALSE?

There exists an upper triangular2脳2 matrixAsuch that A2=(1101) .

Use part (c) of Theorem 2.3.11 to prove part (b): If Ais a regular transition matrix of size n脳nwith equilibrium distribution x鈫�equ, and ifx鈫� is any distribution vector in鈩�n , then limm鈫�鈭�(Amx鈫�)=x鈫�equ.

TRUE OR FALSE?

For every transition matrix A there exists a nonzero vector x鈫� such thatAx鈫�=x鈫�.

TRUE OR FALSE?

There exists an invertible10脳10 matrix that has 92ones among its entries.
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