Mark only correct statements. □ a. If P and Q are orthogonal projections such that PQ- QP, then PQ is an orthogonal projection too. b. Not every skew projection can be diagonalized. c. Any matrix satisfying the equation A = A² is similar to a diagonal matrix. Od. For any two 2 x 2 matrices A, B with complex entries the following formula is true det (A + B)+det(A - B) = 2 det(A) + 2 det (B). □e. For any 2 x 2 matrices A, B with complex entries there is a complex number c such that det (A + B) = det(A)+c-z+z² det (B) for any complex number z.
Mark only correct statements. □ a. If P and Q are orthogonal projections such that PQ- QP, then PQ is an orthogonal projection too. b. Not every skew projection can be diagonalized. c. Any matrix satisfying the equation A = A² is similar to a diagonal matrix. Od. For any two 2 x 2 matrices A, B with complex entries the following formula is true det (A + B)+det(A - B) = 2 det(A) + 2 det (B). □e. For any 2 x 2 matrices A, B with complex entries there is a complex number c such that det (A + B) = det(A)+c-z+z² det (B) for any complex number z.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Mark only correct statements. Please, try to solve this problem as fast as possible!
Transcribed Image Text:Mark only correct statements.
□ a. If P and Q are orthogonal projections such that PQ- QP, then PQ is an orthogonal projection too.
b.
Not every skew projection can be diagonalized.
c.
Any matrix satisfying the equation A = A² is similar to a diagonal matrix.
Od. For any two 2 x 2 matrices A, B
with complex entries the following formula is true
det (A + B)+det(A - B) = 2 det(A) + 2 det (B).
□e. For any 2 x 2 matrices A, B
with complex entries there is a complex number c such that
det (A + B) = det(A)+c-z+z² det (B)
for any complex number z.
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