1) If the null space and column space of a square matrix are orthogonal compleme
ID: 3117579 • Letter: 1
Question
1) If the null space and column space of a square matrix are orthogonal complements of cach other, the natrix must be an orthogonal projection matrix. 5) The characteristic polynomial of a 4 x 4 symmetric matrix must have 4 real roots, counting multiplicity 6) If the characteristic polynomial of A is 2a3-1) and A is diagonalizable, then the rank of A is 3. 7) The dimension of the orthogonal complement of the column space of a square matrix is the dimension of its null space. (8) An orthogonal projection matrix must be orthogonal. 0) The reduced row echelon form of an or thogonal matrix is the identity matrx. (10) Let A and B be square matrices of the same sizo, AB BA, then if A is symmetric so is B.Explanation / Answer
4) true
Column space and null spaces of a square matrix of the orthogonal projection with each other
5) false
Polynomial of a matrix 4x4 real count
6) falseat not multiplicity
7) false
8 ) true
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