Let A3×2 be a fixed matrix with a12 = a31 = 0, but with other entries non-zero. Define T : M3,2 → M3,2 by T(X) = A ◦ X (the Schur-Hadamard product of A and X). What is the range of T? What is the kernel of T? Therefore what is rank(T)? Explain your answers.

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Q: 3. Find x such that the matrix A is equal to its own inverse. 2 -3 A %3D 3

A: Given :  The given matrix is   A = -2-33x To find : We have to find x such that the matrix A is…

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Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

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A: Step 1:Step 2:Step 3: Step 4:

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Q: Let A be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).

A: Recall the following. If A is a n×n matrix and m be any positive scalardet k A=kndet Adet Am=det Am

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A: LU decomposition of the matrix

Q: determine an orthogonal matrix S such that ST AS = diag(λ1,λ2,...,λn), where A denotes the given…

A: A=-3222-3222-3 For eigenvalue λ, pλ=1-λλ+52 To determine: An orthogonal matrix S such that STAS =…

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Q: Suppose that A&B are n x n matrices and A² B = I, then O a. A-1 = BA %3D O b. A-1 = AB %3D OCA-1 = A…

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Q: Consider the linear map T : Rª →→→ R¹, x→→→→ Ax, where [0 2 0 1 2 1 For which a is T one-to-one? A…

A: The given matrix,The aim is to find the values of  for which the linear map  is one-to-one.

Q: -11 36| and P 10] 3 2. Find the diagonal matrix of A = -3 answer -21

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Q: 3. Answer the following questions. a) Determine two numbers s and t such that the following matrix…

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A: The given vectors  and .We have to show that the vector  is in the span for all .

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Q: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

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Q: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

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Q: IK, ar U₁ = 2 vecte U2 = U1, U2, U3 3a + 3 2a +3 a²+3a 7 113 = 4a - 2 3а-1 2a² a) Show that the rank…

A: Introduction: To find the rank of matrix put the matrix into row echelon form and decide the rank…

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

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Q: 3 2 A0 -1 A 1 3 A 0 -2 5

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