Question 14 Suppose that the matrix A has been transformed by some sequence of EROS to the matrix B, where B = 12 3 -2 1 3 1 7 12 (a) det A = 90 (e) none of the above . Choose the correct statement below. (b) det A-90 (c) A does not have to be invertible (d) The rank of A2B³ must be 3

Q: Trace of the matrix =Sum of the Eigen values  True  False

A: Trace is sum of diagonal elements with also equals sum of eigen values.

Q: T2 3] Ssatisfies the relation P2 + =7P where / is 3. Example 70. Show that the matrix P- TO 0215781…

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Q: + Y are invertible matrices of the same size, then X(X¹+Y-¹) Y(X+Y)-¹ = 1.

A: One has to show the said property.

Q: Suppose that an nxn matrix A has a QR-decomposition where

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Q: 13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are…

A: NOTE: Since we can solve at most three subparts in a question, we have solved the first three…

Q: 2.3 Explain how you obtain the matrix N that rotates a point 180° anticlockwise around the point…

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Q: [2 4. Compute the inverse of the matrix A = 3 5 5 in three ways: 1 89 (a) Using the adjoint formula…

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Q: 22 Q.4 Using the matrix: X = 2 4, Calculate: 2 6 M=(I₂ −X(X¹X) ¹X¹) and show that M is a symmetric…

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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: 1(a) Two 3x3 matrices A, B satisfy the relation: A BA=6A+BA. Given: [1/3 A = 1/4 1/7 Find matrix B.…

A: Here we have det (A^-1) = 1/84. So A is invertible and A^-1 exists. Now A^-1*B*A = 6*A + B*A    Or,…

Q: Diagonalize A the matrix A. -27 2 3 4 3+ i√5 0 0 [S+W³² $ "VE] [3+1 0 3-i√√5 i√5] 0 0 [-³+1 0 O…

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Q: The same scenario is used for the remainder of the questions. A psychiatrist clinic classifies its…

A: From the given information, the transition probability matrix is

Q: [-7 12 4 3. Let A = -4 7 Find an invertible matrix S and a diagonal matrix D such that s-1AS = D.

A: The given matrix is A we have to find the diagonal matrix D by finding the eigen value and find the…

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: the matrix A = -5 1 3 -3 Find an invertible matrix S and a diagonal matrix D such that S-¹ AS = D.…

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Q: 2. Find the matrices representing the following geometrical transformations T : R³ → R³, with…

A: All the matrix representation are respect of standard basise1=(1,0,0),    e2=(0,1,0),     e3=(0,0,1)

Q: 2a -3 -1 6. Let Let A = [ [ ²01³ ] , B = [ 3 5 -1 4], - and C =[ ;] 23 3 7 (a) Find all a such that…

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Q: Question 6 The matrix A is the standard matrix for the trans 4² -2 24 4 8 -12 -3 5 01 31 O2 31 ° 27…

A: Given, matrix A is standard matrix for the transformation x→Ax. It transformed 13 in 11 and 27 in…

Q: 2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2…

A: Solution for (a): Show that the matrix �B is nilpotent.Step 1: Understanding Nilpotent MatricesA…

Q: Find the standard matrix for the linear operator on R2 which reflects about the line which has an…

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Q: E3.4. (20) Show that the matrix A= second power of A). [13] is invertible and find A-2 (the negative

A: We have to find .