Let Pg be the matrix whose columns are the vectors in B. Show that PEPB is the n x n identity matrix. (Hint: When you multiply EPg, use that the columns of PB are eigenvectors. When you multiply P(EPg) relate the entries in the resulting matrix to dot products, as in the proof of Theorem 6 from Section 6.2.)

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

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Q: 5. (a) Consider T = LA: R³ - where A is the matrix A = R¹, T(x) = Ax 1 0 0 0 1 0 000 000 (In the…

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Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Find the inverse of the matrix if it exists.

A: Inverse of a matrix A denoted by A-1 is the matrix such that, AA-1=A-1A=I where I is the identity…

Q: 6 0 -1 -3 23*2 4 -3.0 2 4 -5 -13х2

A: As per the question we are given an expression consisting of two 3×2 matrices and their linear…

Q: Find the inverse of the elementary matrix.

A: Now,

Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: ค" ? o - 3 A = %3D 2 -2 -13 %3D

A: We will solve this question using gauss Jordan method.

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

A: Now the transpose is,

Q: The vectors 3 -4 u = -7 = 12 w = -8 -23 + k are linearly independent if and only if k #

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Q: [1 2) 13 · X = 2-

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Q: find the inverse matrix of the matrix

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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: How can we determine the cofactor for each element in a matrix?

A: Query- How can we determine the cofactor for each element in a matrix? Answer-  The first step…

Q: Hi I was looking for this to be expressed as a symmetric matrix

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Q: Solve this question on Matrix

A: ( If you have any queries please feel free to ask me).

Q: 3e sin(6t) -3et cos(6t) SO: 3et cos(6t) 3et sin(6t)

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Q: 6w- 2x -z = 5 6x - 5z = 1 -4x -y + 2z=-7 -2w-x + 3y + 6z = -9

A: Solution:Total Equations are 46w-2x+0y-z=5→(1)0w+6x+0y-5z=1→(2)0w-4x-y+2z=-7→(3)-2w-x+3y+6z=-9→(4)…

Q: How do you find the inverse matrix

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Q: 40. What is the matrix product | 3 ||- 2 1 2] ? F. - 48 24 48] -8 G. -12 8 -16 0 3 4 Н. 1 45 25 6 |-…

A: Matrix multiplication

Q: What is the procedure for obtaining the inverse of a matrix?

A: Given:    Procedure of Inverse Matrix

Q: I need detailed help solving this matrix, please.

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Q: Solve for (A + B^T)*(A^T-B)*C and compute for the matrix inverse of B and AB.

A: Follow the procedure given below.