question number 8 (b) W2 = W,"(c) There are two vectors zjin W1 and zzin W 2such that y = z1+ z(d) y is orthogonal to W, and W2.5. Let W = Span {u}, where u u =Let y =The distance from y to W is(а) 3(b)V3(c) 9(d) 16.Which of the following statements is always true?(а) An n x(b) An orthogonal matrix is orthogonally diagonalizable.(c) If P is an n x n matrix with orthogonal columns, then PT = p-1.(d) Every symmetric matrix is orthogonally diagonalizable.symmetric matrix has n distinct real eigenvalues.27. Find the orthogonal complement of column space of A.(a) null space of A(b) null space of A"(b) row space of A(d) row space of A'8. If A is an nxn square matrix, and I denotes the nxn identity matrix, which of thefollowing statements is not necessarily true?(a) If the columns of A form an orthogonal set, then A is an orthogonal matrix.(b) If AA" = 1, then A is an orthogonal matrix.(c) If A is an orthogonal matrix, its determinant must be ±1.(d) If A is an orthogonal matrix, the linear transformation x→ Ax preserves lengths andorthogonality.9. A is a Hermitian matrix. Then the possible eigen values of A are(a) 5, -5(b)5, -5i(c)5i, -5i(d)-5, 5i10. Let A be a Hermitian matrix. Then, which of the following statements is false?(a)The diagonal entries of A are all real.(b) There exists a unitary U such that U'AU is a diagonal matrix.(c) Eigen values are either real or complex.(b) If A? = I, then A = I.

Name: question number 8 (b) W2 = W,"(c) There are two vectors zjin W1 and zz
Uploaded: 2024-03-05T11:52:21.000Z
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Description: question number 8 (b) W2 = W,"(c) There are two vectors zjin W1 and zzin W 2such that y = z1+ z(d) y is orthogonal to W, and W2.5. Let W = Span {u}, where u u =Let y =The distance from y to W is(а) 3(b)V3(c) 9(d) 16.Which of the following statements