matrix A : n degree matrix matrix B : exchange matrix A's 1st row and 2nd row,                 exchange matrix A's 3rd row and 4st rwo.   now prove  'det(A)=det(B)'

Q: I want to know about change of basis matrix and what does it mean by diagonalization of a matrix.

A: Change of Basis:

Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

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Q: State Triangular matrix?

A: A triangular matrix is a special type of square matrix. It is of two types: Upper triangular matrix…

Q: Find f(B)

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Q: Suppose A is an n x n matrix and B is an invertible n x n matrix. Simplify the following: a) (BAB)?…

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Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

A: The objective of the question is to prove the identity adj(A)^-1 = (1 / det(A))*A = adj (A^-1) for…

Q: e/ By three ways Show that B= %3D isorthogunal matrix

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Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: rmine which of the following matrices is orthogonal. V3 1 (a) (b) V3 0. V3 1- [1 -1 (c) 1 -1 (d) (e)…

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Q: 1 6. Let A = 5 [; ] [:] 3 and B = 1 0 2 (a) Calculate the matrix Aª. (b) Calculate the matrix B-2.…

A: Use the properties of matrix and matrix multiplication to determine the value of each term. The…

Q: Describe all matrices which satisfy det(-A) = -det(A).

A: Assume a square matrix A of order n

Q: Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices…

A: For the given matrices A, B, and C. We have to choose the correct option.

Q: 8. 3 a) Let A = ( 6 1 3 ,B = 6 -2/ %3D 1 Then find the matrix AB. -4 -1

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Q: Let A be a 2 by 7 matrix. Then -A is aby_matrix, and A is a-by-matrix.

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Q: a) Given the matrices A = = i) A-¹. ii) BT if (3AB) = C. = (₁ 2). Find 1 (¹₁3) and C= 3 3 b) If S³R…

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Q: (a) Find the matrix A so that AB=C, where а, а, а, B= b, b, b, & C= b, b, b, a, az az (2 rows are…

A: Given B=a1a2a3b1b2b3c1c2c3 now using row operation R1↔R3 ~c1c2c3b1b2b3a1a2a3

Q: Find the matrix A (in terms of B, C, and D) if (4DA-'B )-1 = C

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Q: For what value(s) of k is the matrix A = 1k1 non-invertible (a) All real numbers. (b) All real…

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Q: [1 2) 13 · X = 2-

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Q: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

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Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: image1

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Q: 2 A= 2 4 3 一 1 -2 1 (i) Find A by using cofactor method. (ii1) Find (4) by using adjoint matrix. 19

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Q: a) Compute the adjugate of the given matrix A and then compute the inverse of the matrix 1 0 2 A = 4…

A: We have to find the adjugate of the matrix A. We know that the adjugate is the synonym of the…

Q: Define invertible matrix.

A: Definition: A square matrix of order   is said to invertible, if there exists an square matrix B…

Q: Examplen' find the pvoduct of the follow ing (wo natricesi 2. 2. ら 1. 又3 3.

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Q: Using only these numbers ( 2,1,9 ) as coefficients, create a matrix of size 5x5 (with all…

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