Given the matrices A = verify that -2 = (²2² ²2² ²1) 3 0 0 1¹) and B = (4 =(-1/₂ 16¹) -2 0 a) (A + B)t = At + Bt b) (3A)t = 3At

Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

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Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Find the characteristic equations of the following matrices: 401] -210 -201

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Q: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find a matrix X that solves the equation 1 2 3 4

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Q: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

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Q: Find the matrix exponential of -3x1 + 8x2 x2 = 12x1 – 7x2 and use the matrix exponential to solve…

A: Given that  x1'=-3x1+8x2x2'=12x1-7x2 and the initial conditions are x10=1,x20=-1 The objective is to…

Q: [2 2 Give two different matrices B so that in each case B 2 2

A: Given matrix

Q: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

A: Step 1:Step 2:Step 3:Step 4:

Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: -3 4 B = -1 | %3D 4 | 0 4 3. C = -2 5 1 D = 4 -2 0 1 Using the above matrices find DB

A: Given matrices are

Q: For each of the following, factor the matrix A into a product QDQ' where Q is orthogonal and D is…

A: A is symmetric matrix ,then A is orthogonally diagonalizable, and Q is the orthogonal matrix, the…

Q: Consider the matrices [2 1 A = 2 2 -2 31 3271 and x = X1 B Xx2 a. Show that the equation Ax = x can…

A: TO solve the system of linear equation we use matrix method .

Q: Find an LU -9 -9 0 2 -45 -63 72 62 L U = factorization for -8 -8 8 8 -104 -111 56 36

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Q: (b) For matrices A = compute following (i) AB and BA -1 -2 1 " B = [ 3² 3], 0 = [-2² 1²/2 41-²-3 and…

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Q: Solve for X using the matrices below. 2A + 4B = -2X 4 -1 0 3 -#-# A = 3 0 and B = 2 0 -4 -1 X = 3-4…

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Q: Consider the two matrices: Compute A + 3B. The result is equal to: Select one: O a. O b. O c. 4 -12…

A: (.)  Given matrices are , A=   2  4-6  0   ,    B =    1 -5-3     2 now we find  12A+3B .