[1 -1 2 12 Let A : -1. Find the matrix B such that (B + I3)-1 = A.

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: What row operation does left-multiplication by the elementary matrix [1 0 0 0] 0 1 0 0 02 10 0 0 0…

A: We have given partially row operated matrix Q asThree types of Elementary row operation:Interchange…

Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: 1 3 -1 For the given matrix A=-2 1 2. Find the inverse matrix ? 053

A: From the given problem:   AT=13-1-212053 So,   A=1-20315-123

Q: Product of matrices multiplication A=[a, b; c, d] x[1,0;0,1]

A: In the question we have to find the product of the matrix.

Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

A: A matrix is diagonalizable if A.m. of each eigen value = g.m. of corresponding eigen value

Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Set up the matrix which will perform the following transformation and write down its character. (x…

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Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: Evaluate the ff. Given: A 1 -1 1 -1 2 3 2 0 y 1 1 -2 4 3 4 1 1 1 -1 find: a. Transpose of matrix A…

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Q: A-Find the value k which make the determinant of the given matrix 10 [k-2 equal to zero k + 3]

A: We need to evaluate the value of k which the determinant of the following matrix equal to zero…

Q: Give a 3 x 3 elementary matrix E which will carry out the row operation (-9) R₂ R₂. E= Test that E…

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Q: Find Jordan form of this matrix

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Q: Prove that An nxn matrix A is non singular if and only if it can be written as a product of…

A: We prove that an nxn matrix A is non singular if and only if it can be written as a product of…

Q: Find the matrix representations for R² and R-1.

A: First we define relation matrix for R:

Q: Find the LU factorization of the following matrix: 203 1 3 1 01 1

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Q: Solve the matrix equation for X: 1 -1 2 – 15 -3 | 0 1| 8 -5 11 i i X =

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Q: 3.) Find the inverse matrix? 2 Use the adjugate of A = 0 -2 1 to find A-1 | 1 0 0 - 2 3.

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Q: Q2: Find the inverse of the matrix M =

A: The given matrix is: M=-312-1 Formula: The inverse of the matrix A=abcd is: A-1=1ad-bcd-b-ca By the…

Q: 1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to…

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Q: Find the determinant of x from the given matrix: 4 -123 2021 10 301 14 2 4 5 -35 -30 -28 -25

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