1. D = [-1 0 1] C=3 4 -1 a) Use the matrices B=2 1 5 9 2 0 3 A 0-2 1 8 -2 to find the values where possible: a6) BTB a4) АВ - С a5) BDT

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 4 4 9 - 3 + X3 3 %3D…

A: We will do this by using definition of augmented matrix

Q: |, and d(A, B) for the matrices in M2.2 using the inner product (A, B) = 2a11b11 + a21b21 0 0 B =

A: We have to find the following given condition

Q: Given the matrices below and that A = LU, solve Ax = b. 1 -2 -3 11 A = -3 -7 b = 33 -4 9 12 –39 [i…

A: We use LU-decomposition method to find the value of x.

Q: Find conditions on a, b, c, and d such that B = as attached commutes with every 2X2 matrix

A: B=abcd Let A=uvxw BA=au+bxav+bwcu+dxcv+dwAB=ua+vcub+vdxa+wcxb+wd Let BA=AB…

Q: If A is m by n, how many separate multiplications are involved when(a) A multiplies a vector x with…

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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: Calculate BA where A and B are the following non-square matrices: 1 3 1 0 3 A = B = 2 %3D 2 1 5 2

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Q: 1 00 0 2 <-5 0 21. 0 0 0 4 22. -3 -4 -3 4 0 0 0 1 -2 1 3 0 3 8 -5, In Exercises 23-24, find the…

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Q: Find matrices P and D so that A = PDP1 and D is a diagonal

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Q: Let A and B be n × n nonsingular matrices. Find nonsin- gular matrices P and Q so that PAQ = B.

A: Given that A and B  are n×n non singular matrices. An n×n matrix A is non singular only if A is…

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: Show that for 2 × 2 matrices A & B the following equation holds. det(A + B)? = [det(A + B)]² Without…

A: a) Show that for 2x2 matrices A and B the following equations hold               det(A+B)2=det(A+B)2…

Q: Find the matrix E so that EB=C, where |1 a2 az 0 B2 B3 a1 a2 dz B= b, b, b, & C= |C1 C2 C3 with a,+0…

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

A: Given: The linear system of equations is, The inverse of a matrix is calculated by using the…

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: Consider the matrices A = [₁, B = 3₁ C= ¹), D=1 K₁ = [5], K₂=[₁²2] Solve AX + BY = K₁ CX + DY = K₂…

A: Concept: We have the matrices A=3211 , B=0110 , C=111-1 , D=11-14 Now the matrices X and Y are…

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

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Q: Suppose A= #B+C where B is symmetric and C is skew-symmetric matrices, 56 B = b12 then byn %3D O a.…

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Q: If the n x n matrices A and B are symmetric and B is in- vertible, which of the matrices in…

A: (16) Given:- A and B are symmetric  ⇒AT=A,    BT=B B is invertible ⇒B-1 exists To prove :- A+B is…

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

A: x+y=1 x-y=2 We need to find the inverse using A-1 =(1/detA)adj A

Q: g.... r, be vectors in R", and let Q be an mxn matrix. Write the matrix Qr, Qr, as a product of two…

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Q: (b).Use the matrices а A d and 5 3 В 4 7 to illustrate Det AB Det BA det A. det B.

A: The matrix AB and  BA are:…

Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

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Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: Use Proposition 2.50 to state Jacobi's method and the Gauss-Seidel method in matrix notation for the…

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Q: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

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Q: The Hill Cypher works in this way: Bob wants to communicate a secrete message to Alice. chose a…

A: Dear Student, Since you have asked multiple questions, we will solve the first question for you. If…

Q: It's given that A,B are invertible matrices and A is also symmetric. If C =BA , D=AB and…

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Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

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Q: Compute for matrix A. matA = matB x matC * [1 B = 2 [3 C -5. 4

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Q: (b) Write the three matrices that are used in Cramer's rule to compute the numerator of the…

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Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

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Q: are the two matrices Simi Siari? If So find B=P'AP 20 030 3 00 A=

A: The solution are next step

Q: Show that AB and 8A are not equal for the given matrices. 11 5 5 AB BA 151/2 1515 1會

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Q: 1090 7, then A alla RA Have the same famk. 40. Prove: If a matrix A is not square, then either the…

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Q: Consider the ordered bases B = {1+x, 1 – x} and B' = {u1, u2} for P1(IR), and suppose that - 2 Q =…

A: Given that  β={1+x, 1-x} and β'={u1,u2} are order bases for P1(ℝ) and            Q=2-145    is the…

Q: Find two unequal 2 × 2 matrices A and B such that

A: The objective is to find two different 2 × 2 matrices A and B such that AB=1001 Let A=pqrs, B=tuvw…

Q: Construct a nonzero 3 × 3 matrix A and a nonzero vector b such that b is in Col A, but b is not the…

A: We will construct A and put b as a linear combination of column vectors in A.

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R, where %3D bị b2 C1 = C2 = 8 b1 what is the…

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Q: Let M,xn be a set of square n x n-matrices. Is the set M„xn a vector Explain. Find 2 different bases…

A: We have to solve given problem:

Q: Show that for matrices A, B E RXn, a vector w = ABx can be written as w = E,(b{ x)a;, %3D :D1 where…

A: Since, A,B∈ℝn×n. ∴ A, B have 'n' rows and 'n' columns with entries as real numbers. The given vector…

Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

A: In a diagonally dominant square matrix, the magnitude of the element corresponding to the diagonal,…