Find the characteristic polynomials of each of the following matrices: (a) ^-]] A = XA(K) = (b) A = 1 2 [3] 0 -5 (c) A = [d] XA(K) = XA(K) =

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: If A = 6. B= [-3 , 2] and C = what is the %3D 3 -2 determinant of (AB – 2C)" ? |

A: Given that  The matrices  To find the (AB-2C)^T

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Q: erify the Cayley-Hamilton Theorem for a general 2 x 2 matrix A, a b -[1]. For a nonsingular n x n…

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Q: Find the determinant of the following matrix (CLO7) ^= [41] Select one: O a. -3 O b. 5 C. -7 O d. 7

A: Given: Matrix:A=[2,5−1,1​​] Calculate the determinant for the matrix. Let`s assume a value for each…

Q: If A and B are invertible 4 × 4 matrices, which of the following statements are always true (i)…

A: To find the true statements of matruces

Q: Find matrix such that 5 3 -1] X+ 2 -3 1

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Q: Write the standard matrices of the given linear operators: a) Lị(x) = (x1 + x2, X2 – X1) b) L2(x) =…

A: a) L1(x) = Ax Let A = abcd Then x1+x2x2-x1= abcdx1x2 = ax1+bx2cx1+dx2 On comparing the coefficient,…

Q: (i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices,…

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Let A, B, and A+B_ all be square invertible matrices of the same size. Show that (A +B')' = A(A+B)'…

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Q: Find ∣A−1∣ for the matrix

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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: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: Prove that the calculate inverse is correct by using the formula I = A(A^(−1))

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Q: 3 4 34 102 228 3) By taking into account the given data, determine the third-order interpolating…

A: If the function satisfies the give data points, this implies that the function curve will pass…

Q: -9 – A 2 Find the greatest value of A that make the matrix A singular. – 6 -2 - A =

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Q: matrix A if (A" – 21)* = } Determine the matrix A if %3D

A: Given,             12AT-2I-1=1234To find : The matrix A.

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: Find the characteristic polynomial of the matrix

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Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

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Q: and (96) = C1 A₁-3+4i with ₁ = Write the solution to the linear system [+] in the following forms.…

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Q: Show that matrix multiplication is associative i.e. A(BC) = (AB)C when- ever the multiplication is…

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Q: The equation A² - 2A + I = O implies that ---Select--- Need Help? Read It ✓. It follows that…

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Q: Rotate the quadratic function 5x^2 + 3y^2 + 2z^2 + 4xz = 14 to its principal axes and express this…

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Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

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Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

A: We have to find equation of line using given information Concept required: Equation of line passing…

Q: Factor these two matrices into A = XAX-¹: 4 = 3 A [

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Q: Find all 2 by 2 matrices that satisfy AA^t=O

A: Since it is given, AAT=0  multiply by A-1 from the left A-1AAT=A-10 AT=0  which implies A is not…