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4. Let A be a square matrix with transpose A". • If AT = A, then A is called a symmetric matrix. %3D • If AT = -A, then A is called a skew-symmetric matrix. (a) Write down an example of a nonsingular 4 × 4 symmetric matrix. (b) Write down an example of a nonsingular 4 x 4 skew-symmetric matrix. ) Use properties of the transpose to show that if B is any m × n matrix, then (c) the matrix A = BT B is symmetric. 'In general, if A is an orthogonal matrix with det(A) = 1, then A is called a special orthogonal matrix. (d) matrix, then In + A+ 2A² + 3A³ is also symmetric. Use properties of the transpose to show that if A is any n × n symmetric

4. Let A be a square matrix with transpose A". • If AT = A, then A is called a symmetric matrix. %3D • If AT = -A, then A is called a skew-symmetric matrix. (a) Write down an example of a nonsingular 4 × 4 symmetric matrix. (b) Write down an example of a nonsingular 4 x 4 skew-symmetric matrix. ) Use properties of the transpose to show that if B is any m × n matrix, then (c) the matrix A = BT B is symmetric. 'In general, if A is an orthogonal matrix with det(A) = 1, then A is called a special orthogonal matrix. (d) matrix, then In + A+ 2A² + 3A³ is also symmetric. Use properties of the transpose to show that if A is any n × n symmetric

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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4. Let A be a square matrix with transpose A". • If AT A, then A is called a symmetric matrix. • If AT = - A, then A is called a skew-symmetric matrix. (a) Write down an example of a nonsingular 4 x 4 symmetric matrix. (b) Write down an example of a nonsingular 4 x 4 skew-symmetric matrix. ) Use properties of the transpose to show that if B is any m × n matrix, then the matrix A = B™ B is symmetric. 'In general, if A is an orthogonal matrix with det(A) = 1, then A is called a special orthogonal matrix. (d) matrix, then In + A + 2A² + 3A³ is also symmetric. Use properties of the transpose to show that if A is any n × n symmetric
Transcribed Image Text:4. Let A be a square matrix with transpose A". • If AT A, then A is called a symmetric matrix. • If AT = - A, then A is called a skew-symmetric matrix. (a) Write down an example of a nonsingular 4 x 4 symmetric matrix. (b) Write down an example of a nonsingular 4 x 4 skew-symmetric matrix. ) Use properties of the transpose to show that if B is any m × n matrix, then the matrix A = B™ B is symmetric. 'In general, if A is an orthogonal matrix with det(A) = 1, then A is called a special orthogonal matrix. (d) matrix, then In + A + 2A² + 3A³ is also symmetric. Use properties of the transpose to show that if A is any n × n symmetric
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Step 1
  • If A is non singular then A is non zero.
  • ATT = A
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