1 1 3 1 6 -1 2 2 1 -2 1 Consider the matrix A = -3 -1 1 4 1 6. 3 i. Find the row space, R(A), and column space C(A) of A in terms of linearly independent rows and columns of A, respectively. ii. Find the bases for R(A) and C(A) in 2 (i) iii. Find dim (R(A)) and dim (C(A)) iv. Find the rank (A)

Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

A:

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

A:

Q: (a) Consider the following matrices: (-2 4 5 -1 4 -5 (4 3 1 3 -3 1 0 4 -1 3 5 2 1 A = ‚B = and C = 3…

A: a) we are given that  A= -24225-154-5; B=43113-2542; C= 104-1353-12533 We need to determine…

Q: Write the dot product of (1, 4, 5) and (x, y, z) as a matrix multiplication Ax. The matrix A has one…

A: Given, A=145, x=xyz Ax=0

Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: Find bases for row(A) and col(A) in the given matrix using AT. row (A) col(A) A = 1 -3 1 0 1 3 1 -4…

A:

Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

A:

Q: A matrix A € Rmxn can also be viewed as a vector, by stacking all its n columns into a single…

A:

Q: (b) Find the projection matrix onto C(A), the column space of A, where A 1 1 12 13 14

A: If columns of A are linearly independent the projection matrix onto columns space of A is P=AATA-1AT…

Q: LOT A = [ ₁ - 10 Let 1 D= 0 1 1 -1 1 Construct a 4x2 matrix D, using only 1 and 0 as entries, such…

A:

Q: Find bases for row(A) and col(A) in the given matrix using AT. 9 0 4 1 4 1 4 8 5 1 8 9 A = 4 -1 3

A:

Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: Find bases for row(A) and col(A) in the given matrix using AT. 3 -9 0 3 1 3 1 37 2 -6 1 6 8 row(A)…

A:

Q: Let X be the 3 x 3 matrix such that left-multiplication by X has the same effect as applying the…

A: In this question we have to find the (1, 2) entry of x.

Q: the solution space of the homogeneous system AX = 0 ) vi. If the system Ax = b is consistent where…

A: We are supposed to solve first three subparts. Given as,

Q: For the matrix A, where 1-30 5-7 002 38 0000 5 0000 0 A = Rank(A) Nullity(A) Dimension of column…

A: We have to find the rank and nullity of A.

Q: Let A be a 6 × 5 matrix with linearly independent column vectors a1, a2, a3 and whose remaining…

A: (a) it is given that A be a 6×5 matrix with the columns a1, a2, a3, a4, a5 and a4=a1+3a2+a3,…

Q: (a) The matrices A and B below are row-equivalent (you do not have to veri. bases for Row(B), for…

A:

Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

A:

Q: Let y = 1 2 and u= 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.…

A: Introduction: The projection of a vector onto another vector is the application of dot product. This…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

A:

Q: Let W be the set of all vectors of the form with r, s and t real. Find a matrix A such that W =…

A: To find matrix A such that

Q: Consider the matrix 1 -1 0 1 -1 -1 4 0 -1 1 1 2 A = 1 -1 2 -2 0 4 2 -2 8 2 -2 Find bases for the…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: Let B = (b1,b2), C={c,c2}, be bases for R2 b,3 (1,1), b, %3 (2,3), с, 3D(1,3), с 2 %3 (1,- 1) Find…

A:

Q: 3. a) A = 26 i) Find the QDQT factorization of A

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: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

A:

Q: Consider the matrix V E R"Xn where V has the structure V = I – 2vvT, the identity matrix I E R"X",…

A:

Q: Consider the 3 x 4 matrix 1 3 1 1 1 2 3 10 1 -1 0 1 A = 4 (a) Find the rank of A. (b) Find bases for…

A:

Q: E A be the matrix given by 3 1 0 1 2 1 A = 3 1 0 トつ (based on the definition of linear…

A:

Q: Consider the matrix 2 -3 -10 3 4 1 -2 0 -1 A 1 -3 1 2 -2 -1 2 -6 4 -4 -2 (la) Find bases for the…

A: We solve the problem using the concept of row reduced echelon matrix

Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find bases for row(A) and col(A) in the given matrix using AT. H 3 -8 0 3 1 -1 3 1 37 2 5 1 6 8 row…

A: Solve the following