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Chapter 2: Q9E (page 107)

If A is a 3脳4matrix and B is a4脳5, then AB will be a5脳3matrix.

Short Answer

Expert verified

False

Step by step solution

01

Multiplication of two matrices

Any matrix of orderp脳qand then B of orderr脳scan be multiplied ifp=rThen resulting matrix is of orderp脳s

Here order (A) =3脳4and o (B)=4脳5.

Then order (AB)=3脳5but not5脳3

02

Final Answer

False

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Most popular questions from this chapter

Which of the functionsf fromR toR in Exercises 21 through 24 are invertible?24 f(x)=x3-x.

There exists a positive integer n such that [0-110]n=l2.

a. Show that if an invertible n脳nmatrix A admits an LU-factorization, then it admits an LDU factorization. See Exercise 90 d.

b. Show that if an invertible matrix A admits an L DU-factorization, then this factorization is unique. Hint: Suppose that A=L1D1U1=L2D2U2, then U2U-1=D2-1L2-1L1D1is diagonal (why?). Conclude that U2=U1.

Let鈥檚 revisit the mini-Web with the graph

1鈬�2鈫�鈫�鈫�3鈫�4

But here we consider the surfing model with a 鈥渏umping rate鈥� of 20%, as discussed in Exercise 2.1.53. The corresponding transition matrix is

.B=[0.050.450.050.050.450.050.050.850.450.450.050.050.050.050.850.05]

This transition matrix is positive and therefore regular, so that Theorem 2.3.11 applies. Use the power method (see Exercise 76) to find the equilibrium distribution. You may use technology. Write the components of x鈫�equas rational numbers.

There exists a nonzero upper triangular 2 脳 2 matrix A such that A2=[0000].
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