1 2 -1 Find the basis of the null space of the matrix A 2 5 -2 (a) < 1, 2>, < 2, 5 > (b) < 1, 0, 1 > (c) < 2, 1, 4 (d) < 1, 2, -1 >

Q: 3 2 0 3 4 0 0 0 2 Let A = Find ALL fixed points of the matrix A-".

A:

Q: -1 1 -2 1 Find a basis for the row and column spaces of A = and find rank(A). 4 -2 3 -9- 3.

A:

Q: 1 -2 4 0 1 1 2 -1 2 5 1 1 4 -1 0 8 0 4 0 -2 1 1 1 -1 0 -2 -1 A = 3 -6 1 2 -4 -4 8 -3 1 -1 1 1 -2 4 1…

A:

Q: -1 6. Let A = 10 0 1 1 3 1 -2 (a) Find the projection matrix onto the column space C(A).

A: Projection matrix onto the column space

Q: 3. (a) Considering an 3 x 3 Suppose, invertible and symmetric matrix A, prove that A-1 is symmetric.…

A: A 3×3 matrix which is invertible and symmetric matrix A. A invertible matrix means thatA≠0 and a…

Q: 3 -2 -2 Verify that A s-'AS = diag(1, 2, 23). -3 -2 -6 is diagonalizable and find a matrix S such…

A:

Q: [1 0 -1] Find a matrix P which transform the matrix A= 1 2 1 to diagonal | 2 2 3 form. Hence A“.

A:

Q: 3. Find the basis of columnspace and nullaspace of matrices: [1 3 1 4 1 -2 3 1 -3 1 3 3 -4 B = -2 -1…

A: The column space is a space spanned by the  columns of the given matrix that correspond to the pivot…

Q: 1 -7 A = 1 2 -3 3 -7 Find an orthonormal basis of the column space of A.

A: The given matrix is                                                  A=1-7-912-339-7

Q: 2 - 2 8 - 20 0 -2 A matrix A= - 2 1 1 reduces to 2 0 – 4 6 1 -9 0 1 3 Find a basis for Nul A: 2.

A:

Q: 4. Consider the matrix A and its echelon form U ~ A given by estua mocvia Cours 17 0 -2 A= -16 0 2 0…

A:

Q: 1 2 1 25 1 3 7 2 2 -2 4 9 3 -1 1 0 1. A = 4 3 0 -4 0 1 -1 0 2. B = 0 0 0 1 -2 0 0 00 0. (a) Find the…

A:

Q: 3 -4 1 For the matrix A = -2 1 -4 determine if the vectors u = 2 and v = are in the null space of…

A:

Q: 1 1 -1 3 Find a basis for the kernel and the image of the matrix A = -2 -1 -1 -2 1 2 -1

A: 1. For any nxm matrix A, the kernel of A ={x: Ax=0} 2. If A is any nxm matrix then the Basis of…

Q: 1 2 -2 1] 6. For the matrix A = |3 6 -5 4 Find a basis for 1 2 3 a) The null space

A:

Q: -1 2 4 Find the 1-norm of the matrix 3 -2 0 1 -1 2.

A:

Q: -2 0 2 ) Let A = Find an invertible matrix U such that UA = R %3D 1 2 3 is in reduced row-echelon…

A: We will use elementary row operation to get U.

Q: 1 7 -2 14 0 The null space for the matrix 3 0 1 -2 3 6 1 -1 4 is span{A,B} where A В ||

A: Given that the null space for the given matrix is span{A,B} .

Q: 1 -1 2 1 | -1 1 3 -1 1 Let, A = -1 3 -6 -2 1 4 3 -1 -5 1 a. Find a 5x5 matrix B such that AB = 0,…

A: Note :- You can cross check yourself to see that AB = 0.

Q: 2 10 3 1 2 3 4 1 0. Let A be a 4 x 5 matrix and its row echelon form A' = 0 0 1 01 Then a basis for…

A: To find the basis for the row space of A.

Q: Question 1: Find a basis for the null space, row space and column space of matrix. Also prove…

A: Apply the following steps, to obtain the basis for the null space, row space and column space of the…

Q: 57-5 A obtarn the matrix P that makes -1 Tts matrit eliagonal 2 -3

A:

Q: [O 1 0 -4] T-2 0 0 -1] A matrix A=6 -2 -20 31 reduces to 0 1 0 0-4 0. -4 | 2 -1 -8 13 4 Find a basis…

A: NOTE: Refresh your page if you can't see any equations. . reduced matrix is

Q: 4

A: According to nullity theorem, rank(A)+nullity(A)=dimension(V)

Q: 41 1 -1 -8- 1 3. -2 Find the basis for the column space of -2 -6 4 a. {0 C. a 3. b. { d. {-1

A:

Q: 1 -1 1 1 1 3 -1 1 Let, A = -2 1 4 -1 3 3 -1 -5 1 -6 a. Find a 5x5 matrix B such that AB = 0, where 0…

A: The matrix given is as follows: A=10-121-113-10-214-133-1-51-6 (a) We will apply row elementary…

Q: 1-2 0 is the reduced row echelon form of the matrix A = 2 čg . Suppose R = |0 0 0 0 1 (b) Find a…

A: Recall:-Let A be a matrixThe non zero rows of matrix in roduced row echelon form are clearly…

Q: |1 -2 4 3 1 1 -1 3 Let A be a matrix which is row equivalent to 0 1 1 0 1 0 0 0 -3 Find a basis for…

A:

Q: -2 11 5 100-10 The reduced row echelon form of the matrix A = Find a basis for the null space of A…

A: Note that null(A)=null(M), where M is in the echelon form of A  and the dimension of null(A) is…

Q: 1 3 -2 Find the basis for the column space of 1 -1 [-2 -6 4 -8 a. {0 1} с. c.{ 3. -21 b. { 0 1} d.…

A: Given: 13-2401-12-2-64-8

Q: 3 4 2 2. A = 1 -9 2 -6 Find an orthonormal basis of the kernel of A.

A:

Q: [1 2 2 4 6 2. Find a basis for the four subspaces of A = |1 2 3 6 9 0 0 1 2 3

A: Given: A=122461236900123             ~122460012300123    R2⇒R2-R1             ~122460012300000…

Q: Basis: Find a basis of the row space of the matrix EE A = 03 -1 -1 3 0 1 -5 1 4 1 0 1 -2 -1 -6 5 -2…

A: First reduce into echelon form then find basis of row space, as in next step.

Q: 2 -2 -4 11. Prove that the matrix A = -1 3 4 is an idempotent matrix. -2 -3

A: A=2-2-4-1341-2-3

Q: 1 - 2 0 1 2 -4 2 4 6 Let A 3 - 6 1 4 1 1 - 2 -2 1 -3 1) Find the rank of A. 2) Find the nullity of…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: Question 1: Find a basis for the null space, row space and column space of matrix. Also prove Rank…

A: Given,

Q: -2 5 -3 1 1 2. Let S = 5 -1 7 Find an orthonormal basis for the space spanned by the -3 -2 -10 -1…

A: Given matrix is: S=-25-3110-175-3-2055-10-1

Q: Proof of Theorem 1.5.3: If A is an nxn matrix, then exactly one of the following happens to the rref…

A: A matrix is in reduced row echelon form, normally abbreviated to rref, if it satisfies all the…

Q: [1 1 -7 -6- A = 1 2 -3 9 -7 Find an orthonormal basis of the column space of A. 3.

A:

Q: -4 1 3 A = 3 -4 2 3 4 -1 -3 A basis for the column space of A is { }

A: The given matrix is:…

Q: 1 2 -1 1 (VI). (12' ) Let A=| 0 2 -1 0 Find a basis for the row space of A and a 1 4 -2 1 basis for…

A: Answer and explanation is given below..

Q: [1 2 3 4 5 (a) Describe the null space of the matrix A = 5 5 55 5 0 2 4 6 8 (b) Express matrix A as…

A:

Q: 4 5 2 5) Consider the matrix A = 2 1 3 0 . Answer the following questions: |-1 3 2 2 5.1) Find a…

A: In this question we have to find basis of null space and dimension of null space.

Q: 1). For the matrix given below. Find a). Basis for row space. b). Basis for column space. c). Rank…

A:

Q: A = 3 1 2 7 -1 4 Find an orthonormal basis of the row space of A. }.

A: The answer is given by using gram Schmidt process as follows

Q: 7 Let K = -1 2 8 0 2 6 3. Express matrix K in quadratic form. -9

A:

Q: [1 2 3] 4 5 6 7. 7 8 9 14. Find a symmetric matrix Q such that q(7) = T" Qu = "

A:

Q: -30 3 -5 Let A = 97 -6 15 263 -24 43 Find an invertible matrix Q and an upper-triangular matrix T so…

A:

Q: 1. Find all real numbers a ER such that the matrix 2 -1 Aa = 1 2a + 2 is diagonalizable.

A:

Q: 2 -1 3 1 8 3 -9 4 -2 1 -3 1 3 -2 3 -9 1 7 3 -1 3 2 -1 Q2) Let A = matrix. Find a basis for the null…

A: