Help determining which statements are true/false: - If a 3x3 matrix A has eigenvalues 1, 2, and 4, then A-2I is invertible. - If a matrix A is a diagonalizable square matrix, then A^3 is also a diagonalizable square matrix. - If an n x p matrix U has orthonormal columns, then UU^T(vectorx)=(vectorx). - If a 4x4 matrix has a rank of 4, then any linear system with coefficient matrix A has a unique solution.
Help determining which statements are true/false:
- If a 3x3 matrix A has eigenvalues 1, 2, and 4, then A-2I is invertible.
- If a matrix A is a diagonalizable square matrix, then A^3 is also a diagonalizable square matrix.
- If an n x p matrix U has orthonormal columns, then UU^T(vectorx)=(vectorx).
- If a 4x4 matrix has a rank of 4, then any linear system with coefficient matrix A has a unique solution.
- For an n x m matrix A and 2
A ∙ vectorx = vector bi inconsistent system, for i = 1,2 --> A ∙ vectorx = (vectors b1+ b2) inconsistent system.
- If A, BB, and C are 3x3 invertible matrices, then (A-B)C is invertible
- vectoru, vectorv orthogonal, unit vectors --> vectoru + vectorv, vectoru - vectorv orthogonal vectors
- If A^2 = - for a 10x10 matrix A, then the inequality rank(A) is less than or equal to 5.
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