Let A be a 9x6 matrix with nullify equal to 1 a) find the rank and nullify of A^T  b) suppose that the third column vector of A, col3 is equal to 0 determine the volume (among col1, col2, ....... col6) that form a basis for the range of A

Q: Let A = [aj be a 4 x 4 matrix. Develop the general expression for det(A).

A: Given:               Matrix A is : [aij] is the 4×4 matrix;   General expression for the determinant…

Q: Find the basis of row space of the matrix A given in the attached image . Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1, R3⇒R3+2R1, R4⇒R4-2R1,…

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

A:

Q: Suppose that a 3×3 matrix A has three columns C1, C2, C3 which span the plane given by x + 2y – 5z =…

A:

Q: Let A be a Hermitian matrix wih eigenvallue A, 2 , 2 · --- > an and ortho normal eigen vecloxs…

A: Since I have solved similar ones ,let me present the solution step by step....

Q: find the Linear trans fromation Tee whose matrix Wzxz i -1 Hi- + =1421] -2 with regard to the base H…

A: Question had typo. Hence solved after correction

Q: A vector is rotated about the Y-axis 45 degrees and is subsequently rotated about the fixed X-axis…

A:

Q: Recail that two nx matrices A and B are Similer if there is an invertible matrie P Such thet p' Ap…

A:

Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Let U be an n × n non singular matrix with non zero diagonal entries. Explain why U must be non…

A: Consider the provided question, Let U be an n x n non-singular matrix with non-zero diagonal…

Q: Let A AL, then the matrix is: neither skewsymmetric Symmetric

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

A:

Q: Let be the skew operator that transforms a 3x1 column matrix into the 3x3 skew- symmetric matrix…

A: Let us consider  3×1 matrix  n=xyz and we have given [ ]x be the skew symmetric matrix…

Q: b) Find an orthonormal basis spanned by a set of vectors V = (2,2,1), V2 = (-2,1,2), V3 = (9,0,0).…

A:

Q: A type (0,4) tensor Tabed satisfies Tabcd A® µ°A°µ¢ = 0 for all con- travariant vectors X and uº.…

A: Tensor of type (0, 4): A tensor of the form Tabcd is called covariant tensor of type (0, 4). A…

Q: Find invertible matricer A and B Cuch th at A+ B is singular. Find cingul ar matrices A and B such…

A:

Q: Let the matrices Ho, H, Ha 1x1 M어ni x [1]. be defined ... the He=L He-I vector of length n-2" can be…

A:

Q: Find a basis for the vector space of all 3 × 3 symmetric matrices. What is the dimension of this…

A:

Q: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula 4 of…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 2. A 2D-subspace (manifold) in 3D- space is defined by the two vectors d;=é,+ê,-2êzand ā,=ê,+2êz-3ê,…

A: A 2D-subspace (manifold) in 3D - space is defined by the two vectors a→1=e^1+e^2-2e^3 and…

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

A: We have to find the Nul(A).

Q: Let W be the Vector space of 3x3 symmetric matrices over R. Show that dim W=6 Please show all steps

A:

Q: If u and v are orthonormal vectors, show that P = uuT + v vT is the standard matrix of an orthogonal…

A: Given: If u and v are orthonormal vectors To Show: P = uuT + v vT is the standard matrix of an…

Q: Let V = Rowz be the vector space of 3-dimensional row vectors and let W = Poly, be the ve following…

A:

Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

A:

Q: orthonormal

A:

Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

A:

Q: Let the n × n matrix A be equal to AT . Briefly describe the pattern of the entries in A.

A: Consider the matrix A of order n×n such that AT=A. let, A=a11a12…a1na21a22…a2n⋮⋮⋱⋮an1an2…ann  here…

Q: Let X and Y be symmetric matrices both size 15x15. Decide if Z = XT(X+Y) is a symmetric matrix too.…

A: Given, X & Y are symmetric matrices. So, XT = X and, YT = Y   Given, Z = XT(X+Y) So, ZT =…

Q: 2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane.…

A:

Q: 7. Prove that the vector length is preserved by orthogonal matrix multiplication. That is , if x E "…

A:

Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

A:

Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=<1,-1,3,-1> and u2=<1,-1,4,2> To Check- If they are…

Q: Let aj be a nonzero column vector of an m×n matrix A. Is it possible for aj to be in N(AT )?…

A:

Q: . Prove that the vector length is preserved by orthogonal matrix multiplication. That is , if x ER'…

A: We have to prove the lemma.

Q: .. Let A = [aij] be a 3 x 3 square matrix such that aij = 1 – |i – j|- (a) Construct the matrix A…

A:

Q: Let A be the matrixx FIRST Find all vectors v so that the distance between Au and the standard unit…

A:

Q: stable

A:

Q: Write x as the sum of two vectors, one in Span fu,,u2,u3} and one in Span (u4}. Assume that (u,.u4)…

A: Two vectors u and v is said to be orthogonal if u.v=0

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: Show that Foranyeigen value Tofthe nonsingu lar matrix A with any natural norm Then

A: Given, Eigenvalue λ of non singular matrix A To prove : 1∥A-1∥≤λ≤∥A∥

Q: 2. If a set of vectors contains at least 2 vectors that are scalar multiples of each other, then the…

A:

Q: Suppose that {v1, v2,..., vn} is a linearly independent set of vectors in Rn. Show that if A is an n…

A: Let's suppose we have a linear relation:…

Q: 2 1 A = 3 -1

A: solve matrix for  AX = 0

Q: 2(b) Th picopert matrix not to Prove matria does r

A: A matrix is defined as a rectangular array of numbers or objects. The arrangement takes place into a…

Q: Find an orthonormal basis spanned by a set of vectors V1 = (2, 2, 1), V2 = (−2, 1, 2), V3 = (9, 0,…

A: We will first find orthogonal basis using Gram-Schmidt Process, then orthonormal basis

Q: 2 -4 1 -7 1 -2 1 -5 6 -12 3 A = -21

A: Compute the standard basis of Nul(A) for the matrix (No need to show work for calculating rref)

Q: Compute the standard basis of Nul(A) for the matrix (No need to show work for calculating rref)

A: Find the Null(A)

Q: Suppose an image is saved as a matrix with a Singular Value Decomposition: A = USVT. Let the vector…

A: Suppose an image is saved as a matrix with a Singular Value Decomposition: A = USVT. Let the vectors…

Q: 7. Prove that the vector length is preserved by orthogonal matrix multiplication. That is , if x ER"…

A: This is a problem of Functional Analysis.