# MATHS----Matrix

posted by .

For a given square matrix A the predicted values of matrix B are:

predicted B=A(A'A)^(-1)A'B

why is the matrix C=A(A'A)^(-1)A' an idempotent and symmetric matrix? and is this matrix invertible?

• MATHS----Matrix -

Assuming (A'A) is invertible, then (A'A)-1 exists.

A(A'A)-1A'
By the property of inverse of product of matrices,
(A'A)-1
=A-1 A'-1

Therefore
C=A(A'A)-1A'
=A(A-1 A'-1)A'
=(A A-1) (A'-1A')
= (I) (I)
=I
after application of associativity and the properties of inverse of matrices.
Since I is idempotent and invertible, so is C.

• Equation of parabola -

The equation of the parabola which contains 2 points (1,1) and (-2,-2) and whose tangent at the point (1,1) has the slope k is y=1/3(A)x^2+1/3(B)x-2/3(C) Express A,B and C with k.Please solve this problem.please

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Matrix

Let A be an invertible n x n matrix, and let B be an n x p matrix. Explain why (A^-1)(B) can be computed by row reduction: [A B] ~...~ [I X] X=(A^-1)(B)
2. ### Math

Fine the size of the following matrix and its additive inverse matrix. Identify if it is a square, column, or row matrix: [ 2 -3 7 1 0 4 ]
3. ### linear algebra

3. Suppose A is symmetric positive definite and Q is an orthogonal matrix (square with orthonormal columns). True or false (with a reason or counterexample)?
4. ### Math

Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. …
5. ### linear algebra

1)If A is an invertible matrix and k is a positive integer, then (A^k)^-1 = (A^-1)^k note: ^ stand for power, -1 stand for inverse of A 2)If A is an invertible matrix, then (transpose of A)^-1 =transpose of(A^-1) 3)Prove A^2 = A, then …
6. ### math

This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in terms of s and r the determinant of R 2. If r=1/3 and s=4 determine the inverse of R 3.State the pair of r and s not including 0, which would make the matrix R a …
7. ### math

This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in terms of s and r the determinant of R 2. If r=1/3 and s=4 determine the inverse of R 3.State the pair of r and s not including 0, which would make the matrix R a …
8. ### science

1 A ……... is a rectangular array of numbers that are enclosed within a bracket . horizontal set vertical matrix 2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is called….. …
9. ### Math

Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other matrix, Matrix B (which is 3 x 4 matrix)?
10. ### Linear Algebra

Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square orthogonal …

More Similar Questions