A) Find all ordered pairs (a, b) such that matrix A is not invertible.\ B) Assume that the values of a and b are such that the equation Ax = e1 has a unique solution. Find only the value of x3 in the solution (in terms of a and b) by using Cramer’s rule.

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: Determine the determinate of x, sin x, cos x by using a 3x3 matrix

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Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: Give example 2. Determinant of a 5 × 5 matrix using properties of determinants

A: The solution of the problem is given in the next steps.

Q: Explain the fact” The determinant is zero when the matrix has no inverse”.

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Q: 3. 3х1 - 2хг -4x1 + 6x2 3 =-5 =

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Q: By evaluating the determinants, verify the addition rule for the 2 x 2 case: a12 a22 la21 a22 la21…

A: Determinate

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: Suppose A is a non-singular matrix. Using properties of the determinant, show that det(A^−1) =…

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Q: Illustrate the multiplying any row (or column) by a scalar do to the determinant?

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Q: 2. Let B = {v₁ =, √₂ =, V3 =, V4 =}. Use determinant to determine whether B is linearly independent…

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Q: 4. Express the following statements in one of the forms P V Q, P ^ Q, or ~ P. Be sure to clearly…

A: (a) Let P be the statement  P: The matrix A has zero determinant  Therefore , the given statement :…

Q: Describe all skew symmetric scalar matrices.

A: Skew-symmetric: A matrix can be skew symmetric only if it is square. If the transpose of a matrix is…

Q: Find the determinant of the matrix, if it exists.

A: The given matrix is 321-1-23. Compute the determinant as follows.

Q: For which matrix we are unable to find inverse, determinant.

A: We have use the matrix property

Q: Give three examples of application of determinant in engineering

A: (1) Determinant can be used to find solutions of the multi variable linear equations.

Q: Solve the matrix by using Cramer's Rule method 2x+5y+2z=10 3x+8y+z=3 2y+5z=1

A: To solve the matrix by using cramers rule method.

Q: Explain how to evaluate a third-order determinant.

A: Consider the provided information, Let A matrix is A=abcdefghi Find the determinant of the matrix.…

Q: Define invertible matrix.

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

Q: Express the determant expression of a 3 X 3 matrix using cofactor and minor, Using this, try to…

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Q: Define the term determinant.

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Q: what is the relationship between determinant and rank

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Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

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