Question

2. Determine if the following statements are true or false. (All matrices are square matrices.) Justify your answers. a) If A contains a row or column of zeros, then 0 is an eigenvalue. b) If 2 is an eigenvalue of A, then (A-2I) is not invertible. c) The eigenvalues of a matrix are on its main diagonal. d) If A is diagonalizable, then the columns of A are linearly independent.

          2. Determine if the following statements are true or false. (All matrices are square matrices.) Justify your answers.
a) If A contains a row or column of zeros, then 0 is an eigenvalue.
b) If 2 is an eigenvalue of A, then (A-2I) is not invertible.
c) The eigenvalues of a matrix are on its main diagonal.
d) If A is diagonalizable, then the columns of A are linearly independent.

2. Determine if the following statements are true or false. (All matrices are square matrices.) Justify your answers.
a) If A contains a row or column of zeros, then 0 is an eigenvalue.
b) If 2 is an eigenvalue of A, then (A-2I) is not invertible.
c) The eigenvalues of a matrix are on its main diagonal.
d) If A is diagonalizable, then the columns of A are linearly independent.

Added by Agust-N G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

This statement is true. If A has a row or column of zeros, then when we multiply A by a vector x, we can choose x such that it has a 1 in the position corresponding to the row or column of zeros and 0 elsewhere. Then, Ax = 0x, which means that 0 is an eigenvalue Show more…

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