Compute the adjugate of A = the cofactor matrix of A. -2 0 3 5 -2 -2 1 2 noting that adj(A) = [cij(A)] where Cij (A) is

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Q: 1.) Let A = Obtain a matrix that is similar to A.

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Q: Using v1 = w1 and v2 = w2 find the standard matrix for these T's: (a) T(vi) = 0 and T(v2) = 3v1 (b)…

A: The linear transformations are defined as: (a) Tv1=0, Tv2=3v1 (b) Tv1=v1, Tv1+v2=v1 To Find:…

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: 4. 5. 6. 7. 8x - 3y (-)-4x + 8y 6rs-7bc (-) 9rs-7bc 5xy - 9cs (-)-3xy + cs x² - 6x + 5 (-) 3x²-2x-2

A: Given :4. 8x-3y--4x+8y5.6rs-7bc-9rs-7bc6.5xy-9cs--3xy+cs7. x2-6x+5-3x2-2x-2

Q: Prove that (a) C(B) C Nul(A), where C(B) denotes the column space of B. (b) rank A + rank B < 5

A: Given that A is a 3×5 matrix and B is a 5×6 matrix. Also AB=0.

Q: 2. Express each of the following quadratic forms as a matrix product involving a symmetric…

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Q: factor of the element 4 in the matrix 1 2 3 A = |4 5 6 [7 8 9

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Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: In how many ways can a group of 3 boys and 2 girls be made out of a total of 6 boys and 5 girls? (a)…

A: Solution: BOYS: Possible combinations of 3 boys from 6 boys ; =C36 =6!3!x6!-3!=6!3!3!…

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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Q: What is the length of arc XY? 45

A: Arc Length Theorem:         The length of an arc of a circle is product of  a ratio measure of the…

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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

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Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: Prove why A-1=(ATA)-1AT is correct using the invertible matrix theorem

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Q: 5) Consider the following matrix: A = 1 2 20 -1 1 030 (i) Compute the adjoint of A. (ii) Use this to…

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Q: Exercise 2. Suppose that A and B are matrices of the same size. Prove the following: (a) (aA)¹ = aAª…

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Q: Calculate the determinant and inverse of the matrices by scaling

A: For matrix A Determinant of A = |A| = 0 As row1+ row2 = row5. Hence |A| = 0 So, inverse of A doesn't…

Q: Find the matrix for T(w) = proj, where = [4 8 -2].

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Q: (4) Find an orthogonal matrix P that diagonalizes A. Verify that PT AP gives the proper diagonal…

A: As per the question we are given a 4×4 square symmetric matrix A and we have to find an invertible…

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

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Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: Find the coordinate matrix of w= 2-3x+x?+x vector relative to base B= {1, 1-x, (1-x)?, (1-x)³} in…

A: Given, w = 2 - 3x + x² + x³

Q: Find the Cofactor Matrix of Matrix B= 3 7 -2 -11 5 8 6 9 -2 4 8 -2 12 20 6

A: We need to find cofactor.

Q: Let x = (−3, 1, 7, 2, 3, − 1)T, find P, Householder matrix, and a scalar a, such that Px = y, where…

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Q: Prove of disprove the statement: If A is a n × n matrix and c is a scalar, then det(cA) = c det(A).

A: The given statement, "If is a matrix and is a scalar, then ".We have to prove or disprove the…