Let W be the set of all 2 x 2 matrices [a b]. d basis for W is S = (a) following questions: (b) • y= X (c) 0 {[][]} ● • S= where, c = 0 and d = 2a - 3b. A || 7 dim (W) = Answer the

Q: Express f in matrix notation where f(ū, 7) = 3x1Y1 – 2x2Y2 + 7x2Y2 – 8x2y3 + 4x3Y2 6x3Y3

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Q: Show that matrices A and B = are inverses of each 2 3 other.

A: See the details solution in below

Q: Q4: Using Cayley - Hamilton theorem to find the inverse of the matrix A, where 1 1 2 A = 3 1 1 2 3 1

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Q: Let A, B, X ∈ Rnxn  be matrices such that det(B) = det(A) − 1 and 3A2 X= XB. Determine det(X).

A: detB=detA-1

Q: Let ū= (a) 2T Calculate projcol Au for the following matrices A: A = - (b) A = 0

A: Column Space: A set of vectors that spans the columns of a matrix A is called the column spaceof A…

Q: Find matrices A and B in M2(Z) such that AB= 0, but BA+0. 3.

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Q: For A 3 1 N² = A. 2 find a 3 x 3 matrix X such that

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Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

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Q: pse chara A, then |E

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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: T a(x¹ B) ax

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Q: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

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Q: Which of the following matrices have characterestic polynomial p(A) = x2 - 10A +1 Select one: a. b.…

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Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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Q: Invert the following matrix 3x – 2y = 9 -x + 3y = 3

A: Solution: Consider the given system of equations: 3x - 2y = 9-x + 3y = 3 The coefficient matrix of…

Q: Find elementary matrices e and e2 such that di 0 e2 = 1 5 1 5 e1 0 dz) for some numbers d and d2.

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Q: Which of the following matrices have characterestic polynomial p(W) =12 – 10A + 1 Select one: а. 1 1…

A: To find eigenvalues and eigenvectors we need to find the characteristic equation for the given…

Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

A: Claim: We have to find E such that EA=Bi.e. E=BA-1 And F such that, FA=C i.e. F=CA-1 A=121312443then…

Q: = 8 -2 7 -9-99 0 2 0 -3 9 3 -1 3 1 -2 6 2 D= O D = 0 B-5÷4 0 0 0

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Q: 2. Write the following functions in matrix form: (a) f(x1,x2, X3) = (x1 + 2x3, x1 + 3.x2 – x3, x1)…

A: Given the function is a fx1,x2,x3=x1+2x3, x1+3x2-x3, x1 In a matrix form…

Q: 9. Find the inverse of the matrix 0 0 k₁ 0 0 k, 0 3 0 0 k₁ 0 0 k₂ 0 0

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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: Which of the following matrices have characterestic polynomial p(A) =A-10A+ 1 Select one: O a. T0 1…

A: To find the correct option

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

A: A Householder matrix is a type of orthogonal matrix that is used to perform Householder…

Q: 3. Prove that (i) /, =1, and (ii) ||, =Vn (I is the Identity Matrix of order n).

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Q: Let A and B be invertible matrices (with the same size). Show that AB is also invertible and (AB)-¹…

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Q: Consider the matrix A 1 2 11 A = |1 5 0 [3 0 5/ Find the adjoint of A. b. Find the inverse of A. а.

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