A matrix, P is called a projection matrix if P2 = P P notequal I Verify that the

Question

A matrix, P is called a projection matrix if P2 = P P notequal I Verify that the following matrix is a projection matrix Find the line that the matrix projects onto. Find the null space of P. Construct a matrix that projects onto the line y = 4x. If is a projection matrix. Find two conditions that the elements of P must satisfy. Are the following sets subspaces of R3. If not explain why not. {(x, y, z)} with x + y + z = 0 {(x, y, z)} with x + y + z = 1 {(x, y, z)} with x = 4y {(x, y, z)} with x > 0 {(x, y, z)} with x = 0 {(x, y, z)} with x = 2r - s,y = r + 2s,z = s for arbitrary scalars r,s. An n times n matrix is symmetric is AT = A and skew metric if BT = -B Dhow that the symmetric and skew symmetric matrices are subspaces of the vector space of n times n matrices What are the dimensions of these subspaces? Show that any matrix M can be expressed as M = A + B where A is symmetric and B is skew symmetric.

Explanation / Answer

a) P2 is not equal to P

So,it is not a projection matrix

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