The set B={[−1010],[00−11],[0002]} is a basis of the space of upper-triangular 2×2 matrices. Find the coordinates of M=[−60−4−5] with respect to this basis.

Q: Let G be a 2x2 matrix with a and b in the top row and 0 and c as the bottom row, where a,b,c are…

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

A: See the details solution in below

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

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Q: Find the (1, 1) entry of the matrix product XY using the matrices below: a X = b and Y = | c 1 -1 d…

A: To find  entry of the matrix product  using the the matrices below. and  and , and .

Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

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Q: Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

Q: 100 A = 0 2 1 022

A: The matrix A3×3 can be represented as a product of LU=A where L=100l2110l31l321 and…

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: Let V = [- 7, – 7,0] and V½ = [0, 3, – 4]. Use the Gram- | Schmidt procedure to construct an ordered…

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Q: Consider the following (real, symmetric) matrix: A-(10 40 = 40 158 Determine the real canonical form…

A: Given:  A=104040158 To find the real canonical form of a given matrix.

Q: Consider the following matrices A, B and C (attached in image). Note that only the entries of matrix…

A: Since there are more than one questions, so find the solution of the first question.

Q: 2. Compute both AB and BA for the following matrices, and observe that AB + BA: -1 [] B= B-[83] and

A: To compute AB and BA for the following matrices, and to observe that .

Q: Find a 2 x 2 matrix such that [3]==1] (incorrect) 4 -2 -2 Answer(s) submitted: C

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Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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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: For matrices A, B, and C, if A is invertible and AB-C, then True False B = CA-¹.

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Q: Use the following matrices to find the sum and product of A and B. [: 3 1 0 -2 0 1 A = 2 -5 4 B = 4…

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Q: Consider the bases B1 = {(1,2), (- 3,0)} and B2 = {(3,2), (- 1, –2)} of R. The input to "(2.1)' of…

A: Consider the given vectors. B1=1,2,-3,0B2=3,2,-1,-2 Express the vectors in linear combination.…

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 .

Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…