4. Find bases and dimensions of the fundamental subspaces associated with the matrix 1 2 1 3 A = 4 2 -2 1 3 2 6. -6 -

Q: Please create an example of a m x n square hermitian matrix (m=4, n=4 ). Use Gram-schmidt process to…

A: To give an example of 4 x 4 Hermitian matrix. And to solve the orthogonal bases for each fundamental…

Q: 1. Find a basis for the vector subspace of 2 x 3 matrices given by а 6 c V := { : a + b+ c= 0, a = c…

A:

Q: Find the orthogonal projection of 9. -3 = 4 onto the subspace W of Rª spanned by -3 -4 3 and 6 -3…

A: Solution:-

Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: If the subspace of all solutions of Ax = 0 has a basis consisting of seven vectors and if A is a 7x9…

A: Given Ax=0 has solution subspaceof basis consisting 7 vectorsNoteThis x are belong to null…

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, -5), (1, 3, –2,…

A:

Q: Suppose A is 10 by 10 and A2 = 0 (zero matrix). So A multiplies each column of A to give the zero…

A:

Q: 10. Find a basis for the subspace spanned by the given vectors. What is the dimension of the…

A: Given vectors  1-32-4,-39-612,2-142,-45-37 we have to find    (a) Basis for the subspace spanned by…

Q: Find a basis for the subspace of IR spanned by the following vectors. 6. 10 1 1 -2 -6 -10

A: We will reduce the dependence of the set by checking if (and how many) any vectors are dependent on…

Q: §5.1, Exercise 17. For which scalars a, b, c do the solutions to the equation ax + by = c form a…

A: We have to find for which scalars a,b,c do the solutions to the equation ax+by=c from a  subspace of…

Q: [1 Let matric A be a square hermitian matrix= |2 4 5 5 1. L3 Use Gram-Schmidt process to find the…

A: Consider the given matrix, A=123235351 Let u1=123, u2=231, u3=351 Step 1: u1=v1 v1=123 Step 2:…

Q: Find a basis for the subspace of Rª spanned by S. S = {(29, –14, 6, –12), (-14, 7, –3, 6), (4, –2,…

A:

Q: 7. The set of all 2 × 2 upper triangular matrices is a subspace of M2,2 . a. True. b. False.

A:

Q: Find the orthogonal projection of 5 -19 -6 onto the subspace W of R* spanned by 4 4 and 1 -2 3 projw…

A:

Q: Suppose that A is an n x m matrix of rank 5, the nullity of A is 4, and the image of A is a subspace…

A:

Q: 1. For each matrix 8. a) 4. 1 13

A: Hey there the time bound provided to solve a single question is not enough to solve each part of the…

Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the  vectors that it is linearly dependent or linearly independent.  If the vectors…

Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: If the subspace of all solutions of Ax 0 has a basis consisting of two vectors and if A is a 5x7…

A: The matrix A is a representation in the standard basis of the linear transformation, f:ℝ7→ℝ5, x↦Ax

Q: 3. Without computing A, find bases for the four fundamental subspaces if: [1 0 0 6 1 0 9 8 [1 2 3 4…

A: Answer is mentioned below

Q: 2) Find all the invariant subspaces of the following matrix 0. 1 0 1 1 1

A: Given matrix is, Let, A=010010111 Now, calculating the eigen value of the given matrix.…

Q: Find a basis for the subspace of R* spanned by S. S = {(2, 5, -3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A: The given set,S=2,5,-3,-2, -2,-3,2,-5, 1,3,-2,2, -1,-5,3,5

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 9, -2, 53), (-4, 2, 4, –2), (8, –4, –8,…

A:

Q: 5. The solution set of the system Ax 0 with three unknowns is a subspace of the vector space M33 O…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -4), (-2, –3, 2, -5), (1, 3, –2,…

A:

Q: 10 Find the projection of 69 -15 -4 subspace W of R³ spanned by -6 and - 14 onto the √] 6 -

A: Given v→=10-14-15 The objective is to find the projW(v→).

Q: If A is an n x n matrix such that A = - A' and all of the eigenvalues of A are 0 or 1, then A is the…

A:

Q: Linear algebra

A: Consider the set

Q: -11 -3 1 2 Find the orthogonal projection of v = onto the subspace W spanned by 43 -5 -3 3 4 5 projw…

A: Given: v→=-11243-3 and W is a subspace spanned by -32-53, -3254, 12-35.

Q: 7. The set of all 2 x 2 upper triangular matrices is a subspace of M22- a. True. b. False.

A: Use two step test of subspace to solve this problem.

Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

A:

Q: If the subspace of all solutions of Ax = 0 has a basis consisting of seven vectors and if A is a 5x9…

A: Given that  The subspace of all solutions of Ax=0 has a basis consisting of seven vectors. A is a…

Q: Find a basis for the subspace spanned by the given vectors. 3 Span 3 -1,2 1 3 4

A: The given subspace consist of all vectors in Span-231, 3-12, 123, -154. Take S=-231, 3-12, 123,…

Q: (a) If a 7 by 9 matrix has rank 5, what are the dimensions of the four subspaces? What is the sum of…

A: Use the given information.

Q: 7. Find a basis for, as well as the dimension of the subspace of R* generated by the vectors (1, -1,…

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: 4) Find a basis for the subspace of R' spanned by the vectors. {(1,1,0,0), (0,0,1,1), (-2,0,2,2),…

A: We have fond the maximal linearly independent subset of the given set.

Q: 1. Consider a 12-by-9 matrix of rank 7. What are the dimensions of the four fundamental subspaces…

A: Let A be the matrix of dimension 12-by-9, with rank 7. Since the rank of A is 7, the number of…

Q: 4. Find a basis for the intersection of the subspaces V = Span ((1, 0, 1, 1), (2, 1, 1, 2)) and W =…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(3, -2, -3, 6), (2, –2, –3, 6), (-1, 1, 1,…

A:

Q: Find bases for the four fundamental subspaces of the matrix A. 1 4 9 A = 0 8 0

A:

Q: (Strang 3.5.14) Without computing A, find bases for its four fundamental subspaces: [1 0 0] [1 2 3…

A: Assume that the matrix, A=LU.   Matrix L has pivots in column 1, 2, and 3, therefore Column space:…

Q: Find a basis for the subspace of R" spanned by S. S = {(43, -21, 6, 18), (-14, 7, -2, -6), (6, –3,…

A: Subspace of  ℝ4  spanned by S is               S = { (43,-21,6,18) ,(-14,7,-2,-6) ,…

Q: If the subspace of all solutions of Ax = 0 has a basis consisting of three vectors and if A is a 7x9…

A: The solution is given as

Q: Find a basis for the subspace of R“ spanned by S. S = {(2, 5, –3, –5), (-2, –3, 2, –2), (1, 3, -2,…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -5), (-2, -3, 2, -4), (1, 3, -2,…

A: We have to find the basis.

Q: 1 3 6. (4) (a) Find orthonormal vectors ĝ1, 2 in the subspace Span{a, b} spanned by ä = 7 of R5. 1…

A:

Q: Find a basis for the subspace of R* spanned by S. S = {(2,5, -3, -2), (-2, -3, 2, -5)(1,3, -2,…

A:

Q: 1. Consider a 12-by-9 matrix of rank 7. What are the dimensions of the four fundamental subspaces…

A: 1.  The four fundamental subspaces associated with any matrix are column space , row space , null…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.