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Chapter 2: Q27E (page 108)

Question:TRUE OR FALSE?

The matrix product(abcd)d-b-ca is always a scalar multiple of l2.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Invertible matrix

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

02

Compute the product matrix.

Consider the system of matrices.

(abcd)(d-b-ca)

Compute the product.

(abcd)(d-b-ca)=ad+b-ca-b+bacd+d-cc-b+da=(ad-bc00ad-bc)=ad-bc(1001)

Here, the scale is,ad-bcl2

Hence, the given statement is true

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Most popular questions from this chapter

TRUE OR FALSE?

There exists an invertible2脳2 matrix A such thatA-1=-A.

Consider an invertible n脳nmatrix Aand ann脳nmatrix B.A certain sequence of elementary row operations transforms AintoIn.

a. What do you get when you apply the same row operations in the same order to the matrix AB?

b. What do you get when you apply the same row operations toIn?.

TRUE OR FALSE?

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

Which of the functions f from R toR in Exercises 21 through 24 are invertible?22 f(x)=2x.

Give a geometric interpretation of the linear transformations defined by the matrices in Exercises16through 23. Show the effect of these transformations on the letter L considered in Example5. In each case, decide whether the transformation is invertible. Find the inverse if it exists, and interpret it geometrically. See Exercise13

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