In Exercises 11 and 12, use an inverse matrix to find [x] for the given x and B 11. 3 -4 = = {[³] [4]} -5 6 2 X = 2 -6

Q: Show that matrices A and B = are inverses of each 2 3 other.

A: See the details solution in below

Q: Find the difference. See Examples 6–7. 2x3 + 7x2 – 3x + 7 6x3 – 4x2 – 9x – 3 -

A: In order to subtract 2 polynomials, subtract like terms . Like terms are the terms with equal degree…

Q: З and an - - 3ап-1 + an-2 for integers n>2. Evaluate and d4: Let a, = 2, a2

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Q: 1 −1 1 -2 1 2 1 −1 -1 0

A: The given matrix,The aim is to find the inverse of the matrix.

Q: 1. Perform the following matrix operations, if possible: (a) 89+1671 X 3 5 3 - 0-6

A: We have to perform the matrix operations if possible.

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: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

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Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

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Q: 2 1 }], 3

A: LetWe have to find the inverse of the above matrix.We know that

Q: How do you find the inverse of this matrix?

A: We first find the determinant of the matrix to check if the matrix is invertible or not.

Q: (1 2 -3 1 -3 0 3 2 4X=| 10 2 7 2 -1 0 10 7 8

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Q: Use the given definition to find f(A): If f(x) = a, + a,x + a,x2 + ... + a,x" is a polynomial…

A: We have to find f(A).

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: Write the standard matrices of the given linear operators: a) L1(x) = (X1 +x2, X2 – X1) b) L2(x) =…

A: a. we have L1(x)=(x1+x2,x2-x1)  we take standard ordered basis β= (1,0),(0,1) and β=…

Q: The mathematics department of the College of Science consists of four people: Josie who is…

A: Using the logical assertions presented, we must derive the hobbies associated with the individuals.

Q: -2 - Find the inverse of the matrix A = 6. or state that there is no inverse. 4.

A: A necessary condition for the inverse of a matrix that it must be a non-singular matrix.

Q: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

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Q: Homework : Find the inverse of the matrix and verify that A-'A = A A-1 = 1,

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Q: Define Matrix Inverse?

A: The inverse of matrix A with order 2×2 can be obtained by elementary row operation on a new matrix…

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 inverse of the matrix if it exists, A= 2 4 1 -1 1 -1 1 4 0

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Q: Find the inverses of the matrices in Exercises 1-4. 1. 8 3 [5 2

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Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

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: How would I write the following 2 functions in matrix notation? Q(h) = (h, 2h, 3h) F(x, y, z) =…

A: We have to write the function as matrix notation. The given function is Q(h) = (h, 2h, 3h) Clearly,…

Q: Anxn be an invertible square matrix. Show that cofactor(A)=A The formula of matrix inverse you might…

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Q: Find the inverse matrix of [2 1 -1

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Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

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Q: Solve the matrix equation for x -2 1 4 3 2 1 -1 -1| X = 6. 7 8. 9. 1 1 -4 1 3 7 9.

A: The solution is given in the next steps.

Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…