Consider the following matrices: 3 2 6 1 1 -3 A = -6 3 2 and...

 

Transcribed Image Text:

Consider the following matrices: 3 2 6 1 1 -3 A = -6 3 2 and B = 0 -4 2 6 -3 -3 -4 -2 1.1 Use the definition below to determine whether the matrix A = A is orthogonal. Definition: A matrix is orthogonal if its transpose is equal to its inverse. Instruction: Use the Gauss-Jordan elimination method to compute the inverse of A. 1.2 Determine whether the matrix B is singular. 1.3 Use the definition below to determine whether the matrix B is positive definite. Definition: A square matrix M of order n ≥ 1 is said to be "positive definite" if it is symmetric and if x Mx > 0 for all non-zero column vector x = [x1 x2 xn] On. 1.4 Use the definition below to determine whether the matrix A is idempotent. Definition: A square matrix X of order n ≥ 1 is called an idempotent if X² = X. (6) (2) Consider the following matrices: 3 2 6 1 1 -3 A = -6 3 2 and B = 0 -4 2 6 -3 -3 -4 -2 1.1 Use the definition below to determine whether the matrix A = A is orthogonal. Definition: A matrix is orthogonal if its transpose is equal to its inverse. Instruction: Use the Gauss-Jordan elimination method to compute the inverse of A. 1.2 Determine whether the matrix B is singular. 1.3 Use the definition below to determine whether the matrix B is positive definite. Definition: A square matrix M of order n ≥ 1 is said to be "positive definite" if it is symmetric and if x Mx > 0 for all non-zero column vector x = [x1 x2 xn] On. 1.4 Use the definition below to determine whether the matrix A is idempotent. Definition: A square matrix X of order n ≥ 1 is called an idempotent if X² = X. (6) (2)