Q. No. 3 a) If a n x (n + 5) matrix has rank n, find dim Nul A, dim row A and rank AT. where n is last digit of your arid number. If your arid id is 19-Arid- 1121 then n=1. b) Find values of h for which the vectors are linearly dependent. Justify your answer. 1 31 -1 -5 4 7 h

Q: 3. Given a vector x = (0 4 a), where a is the last digit of your Roll number. Find a Householder…

A: Given that x=0 4 7T. The Holder matrix is given by Hx=I-2xTxxxT Hence the Holder matrix is…

Q: b) Determine the matrix A for the linear transtormation which means that the vectors Of the room are…

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Q: Q2 Let A be a 4 × 5 matrix. If the column vectors a1, a2 and a4 are linearly independent and satisfy…

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Q: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

Q: Calculate the condition number of the matrix using the Frobenius norm. [1 104 3 (a) Is the problem…

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Q: 1 3 14. For the vector b=b, to be in the row space of the matrix A= then 256 by . by-4bz +1 lb, = 0…

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Q: Let A be an 2 x 3 matrix and b be a vector in R? such that the system Ax = b has solution set 0. +t…

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Q: Answer considering the matrix with the given vectors as its columns

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Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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Q: 5. Give 2 x 2 matrices A so that for any x e R² we have, respectively, (f) Axis the vector obtained…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A be a matrix 5 * 5  We have to find the matrix A and also find the geometric description of A and…

Q: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: Let x and y be distinct vectors in Rn (i.e., x = y), and let A be an n × n matrix with the property…

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Q: [1] Construct a 3 x 3 nonzero matrix A such that the vector |2 is a solution of 3. Ах 3D0

A: A vector is given let x=123 To find: A non-zero 3×3× matrix,A=a11a12a13a21a22a23a31a32a33

Q: Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is…

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Q: 3.2. Determine, if the vectors (9000 (:) (3) 1 1 1 1 1 1 1 1 are linearly independent or not. Do…

A: To determine a set of vector is linearly independent then determinant must be non zero.

Q: 10 The matrix that rotates the vector to the vector in the counterclockwise direction is given by:…

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Q: Show that if A is a mxn matrix and rank(A)=m then Ax=b has a solution for any vector b in Fm (Hint:…

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Q: 4) The Cayley-Hamilton Theorem states that every square matrix satisfies its characteristic…

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Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R°…

A: System of Linear equations

Q: Answer considering the matrix with th e given vectors as its columns

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Q: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

Q: 9.M.4 Let A = AT be a symmetric matrix, λ be a real number, and v₁ and v2 be vectors such that Αυγ =…

A: It is finite dimensional vector space, so an inner product can be imposed.

Q: 4) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.5., # 24, or from your…

A: see below the answer and explanation

Q: 6. Consider the 3-dimensional vectors El a = 2 and Find a matrix P for which, for each 3-dimensional…

A: 6) Given two vectors are a1=122 and a2=102 .

Q: Let A be an 6 x 4 matrix and b be a vector in R® such that the system Ax = b has solution set +t 1…

A: The general solution of the given system Ax=b is given as  x1x2x3x4=1-41-9-7+s-9-79-3+t2371 I know…

Q: 3. Consider the following linear system: A7 = 8, where 1 1 1 A = 1 - 1 and 1 -1 (a) What is the…

A: To prove the system is inconsistent, just convert the given system into equations and try to find…

Q: 2. Using Gauss-Seidel, compute a solution to the problem Ax=b where A is an nxm matrix of the form A…

A: Given: The matrix is A=2-100⋯-1-12-10⋯00-12-1⋯0⋱⋱⋱0⋯0-12-1-10⋯0-12. To find: The solution of Ax=b…

Q: Find the dimension of the null space and the dimension of the column space of the -3 -2 7 7 [1 -27 2…

A: The given matrix, M=1-3-277-22-6-45147 we have to find dim(Nul(M)) and dim(col(M))

Q: 31. Let A be a 5 ×7 matrix with rank 4. a. What is the dimension of the solution space of Ax = 0? b.…

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Q: Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are…

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Q: (3) If A is a real 2 by 2 matrix, A-(::) a b and a is a two-dimensional column vector, what…

A: Please check step 2 for the solution.!

Q: 1 %This program accepts the concatenated column vectors A, where the size of the Matrix will…

A: *Answer:

Q: Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1,…

A: Given: The order of the matrix A is m×m. The row vectors are a1,a2,a3,.....am and the dimensional…

Q: 2. (a) Give an example of a non-invertible non-zero 2 x 2 matrix A with entries chosen from the set…

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Q: of the null space and the dimension of the column space of the -6 8 12 3 -47 2 12 4 -6 6 -8 (a)…

A: We know that  rank(M) = dim( Col(M))

Q: Generate a matrix A by settingA = floor(10 ∗ rand(6))and generate a vector b by settingb = floor(20…

A: Generate a matrix by setting A = floor(10*rand(6)) and a vector b by setting b = floor(20*rand(6,1))…

Q: 5. (a) Show that the columns of the matrix B below span R*. 1 1 0 2 1 3 0 3 0 2 3 3 0 0 6 5 В (3)…

A: See the attachment

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Q: Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are…

A: Linear Dependence: Let A = v1, v2,…, vr be a collection of vectors from ℝn . If r>2 and at least…

Q: 2. Find a 3 x 4 matrix R for which the ill space of R is spanned by the vectors Hint: try to set up…

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Q: Suppose that A is a square matrix and that ∥Au∥ = 1 for all unit vectors u. Show that A is…

A: Given: To show that A is orthogonal, assuming that A is a square matrix. Here Au =1for all unit…

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A: I have checked one by one option wise

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A: M = 0 will be the right answer.

Q: 3) If x=[2 6 12; 15 6 3; 10 11 11, then: a) Replace the first row elements of matrix x with its…

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Q: Let A be an 2 x 3 matrix and b be a vector in R" such that the system Ax = b has solution set 0. 0.…

A: Given: The system Ax = b has solution set 395+s30-7+t072.

Q: Which of the following statements is/are correct? Please select one or more: The approximate…

A: The approximate solution of x1+x2+x3x1x2+αx3=1=1=5 linear equations cannot be found for α=1 by the…

Q: 7. Consider the vectors 3 –2 -1 -1 4 2 W2 = 1 V2 = W1 = 4 1. and suppose that A is a matrix such…

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Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

A: