Let A, B, C be invertible matrices of order 3x3. Show that if AB = AC , then B =C. %3D

Q: Verify AB = BA for the matrices below.

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Q: if A and B are matrices and K is a scalar

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Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: Find the rank of the matrices where x, y, and z are distinct.

A: We have to find the rank of the matrix

Q: If A and B are invertible matrices, show that AB and BA are similar.

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Q: Find ∣A−1∣ for the matrix

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Q: Let A and B be the following matrices. Perform the following operations: A. B = B. A = -37 67 28 -26…

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Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: In Exercises 19-20, find the inverse of each of the following 4×4 matrices, where k₁, k₁, k3, k₁,…

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Q: find if the vector x is in the range for matrix A

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Q: Give a matrix A and vector b so that Ax = b has no solution, but Ax = b has many least squares…

A: For first part consider an example which is following :Here  has no solution, but  has many least…

Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: 3 - 3 1 /- 1

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Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: Find the meet of the zero-one matrices A and B if A=⎛⎝⎜110010101⎞⎠⎟ and B=⎛⎝⎜011100111⎞⎠⎟.

A: MUST KNOW: In a zero -one matrix all elements are either 0 or 1 and represent false and true…

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: Finding the Determinants Using Combined Methods (row operations and cofactor method) -2 -4 A = 1 4 8…

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