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Chapter 5: Q17E (page 233)

Question: If the n脳nmatrices Aand Bare symmetric and Bis invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well?role="math" localid="1659492178067" B-1.

Short Answer

Expert verified

The Matrix is A + B symmetric.

Step by step solution

01

Definition of symmetric matrix.

A square matrix is symmetric matrix ifA=AT

02

Verification whether the given matrix is symmetric.

Given that A and B are symmetric matrices and B is invertible.

Since A is symmetric, A=AT.

Then by properties of transpose,A+BT=AT+BT it has

A+BT=AT+BT=A+B

Therefore, A + B is a symmetric matrix.

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Most popular questions from this chapter

Question: If the n脳nmatrices Aand Bare symmetric and Bis invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well?A+B.

Use the various characterizations of orthogonal transformations and orthogonal matrices. Find the matrix of an orthogonal projection. Use the properties of the transpose. Which of the matrices in Exercise 1 through 4 are orthogonal? [0.60.80.80.6].

If Ais ann脳mmatrix, is the formulaim(A)=im(AAT)necessarily true? Explain.

Find the length of each of the vectorsv鈬赌In exercises 1 through 3.

  1. v鈬赌=[711]

Complete the proof of Theorem 5.1.4: Orthogonal projection is linear transformation.
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