Q₁: Q: When possible, find an invertible matrix P& M₂ (K) such that PAP-¹ is a diagonal matrix where Ú) A = (1) A = (V) A = -2 2 -3 (²1²²) - -2 2 1 C O 3 -2 3 -2 <-2 3 O -2 3 : ₁₁A= lº (iv) A = 2 1 2 1 8 -14 2 2 -2 3 ;)

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: Find a 2 by 2 matrix that reflects the point (x,y) abot the x axis?

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Q: Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3…

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Q: Determine the determinate of x, sin x, cos x by using a 3x3 matrix

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Q: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

A: here question has a mistake , though I correct it and solve it for you, here two different f(x) is…

Q: R2 → R3 first performs a horizontal shear that transforms  and then reflects points through line x2…

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Q: 3. Let B = {[4] [7]} and c={[7][7]} 4 9 C a. Find the change of coordinate matrix from C to B.

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Q: 9. A = -2 2

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Q: Find 3 x 3 upper triangular matrix with determinant 1.

A: 3×3 upper triangular matrix

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: Determine the real number values of the constant a with which the matrix A= (14 a1)  is positive…

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Q: Compute(Ax - y)||2, where A = Rm×n is a matrix and x ≤ Rª and y ≤ R™ are both vectors .

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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…

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Q: Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite,…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

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Q: for a matrix A 3 6 2 5 if f(x)=(x+2)(x-2), calculate f(A)

A: Given: Matrix A=3625 To Find: f(A) when f(x)=(x+2)(x-2)

Q: Find the characteristic equation of the given matrix: 8. -D1 2 0. A = 8 -D1 6 -6 1 6 5 Select one: O…

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Q: Solve the matrix by using Cramer's Rule method 2x+5y+2z=10 3x+8y+z=3 2y+5z=1

A: To solve the matrix by using cramers rule method.

Q: Take the system æ' = 10x? + 10y2 + 9xy, y' = e10x + 10y?. The Jacobian matrix is help (formulas)…

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Q: (2a, Let A be a 3 × 3 matrix b b a A = a a a a a Show that A is invertible if a +0 and a + b. (2b,…

A: We need to prove and find value of c

Q: Write down the 3 x 3 matrix that rotates a 2D point by angle about a point 0 p = (xp, yp).

A: Consider point .To write the  matrix that rotates a  point by angle  about a point .

Q: Express the quadratic equation in the matrix form x Ax + Kx + f = 0, where a Ax is the associated…

A: The given quadratic expression is .We need to convert this quadratic in the form .

Q: 4. Evaluate the determinant of the matrix by using a convenient column or row. (a) 3 -1 3 1 A = 2 0…

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Q: (d) Express 2 as a linear combination of Y1 (e) Express 2 as a linear combination of L93 (HB)). (0)…

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Q: -1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B²…

A: If A and B are nxn invertiable matrices then(AB)-1=B-1A-1