1 2 3 Let A = 3 5 .What is the value of z if A is not- 1 invertible? 2.

Q: 4 Let A b [² }] Find Conditions on 1 c d a,b,c and d that AX =0 that AX=0 has infinitely many…

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Q: 11. Every line in R" is a subspace of R". 12. Every line through the origin in R" is a subspace of…

A: This is a problem of linear transformation.

Q: 3. 6. 7 # 4. Let A 2 3 What is det(A), the determinant of A? 4 (A)0 (B) – 5 (C) 5 (D) – 24 (E) 24

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Q: 3 5 2 -1 -7 -3 -3 2 1 2

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Q: |1 2 3 0 1 1 1 (g) 0 0 1 3 100 2

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Q: Compute the determinant using a cofactor expansion down the second column.

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Q: Consider a square matrix A having characteristic polynomial p(A) = (1 + 1) ^ 2 (A - 2)(^ – 3) ^ 2 a)…

A: Dimension of a matrix : Let A be a square matrix with n rows & n columns .So its dimension is…

Q: Corollary. Let A E M,(F). Assume that its characteristic polynomial is a product of linear…

A: When the dimension of eigenspace of a matrix equals the dimension of the matrix, then it is…

Q: Compute A² and A³. Make a prediction for A5 and Aª: 1 b 4 = [] and 4= [²2] A A [33].

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Q: (2 3) Let A = Verify the Cayley-Hamilton theorem. Use the theorem to express 1 2 A² and A3 as linear…

A: The given matrix is A=2312. Cayley-Hamilton theorem: Cayley-Hamilton theorem states that, "Every…

Q: 4. Find the determinate of [A]. 3 2 [4]= -3 -10 -3 -10 10

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Q: Compute the determinant using a cofactor expansion across the FIRST row. (read carefully)

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Q: Let A = 123 456 Which of the following is TRUE

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Q: 14 in. 2 in. 2 in. → 3 in. 3 in. The volume of the figure is cubic in. Enter

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Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

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Q: 6. Find the value of x, y and z using Cramer's Rule and Gauss-Jordan Method. X+y+z 12 2x + 5y-3z 6…

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Q: 2. Let 4 2 2 A = |-2 -1 -2 2 -1 Use any method from class to determine if A is invertible. If A is…

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Q: 1. Consider M = 1 23 234 47 a Compute |M| according to the definition of determinant.

A: The given matrix is

Q: 8. TRY THIS. Use the theorem on bounds to establish the best integral bounds for the roots to x +…

A: 8. Given,              x3+3x2-5x-15=0

Q: If A is a square Matrix such that A'-A, what are the possible values of det A?

A: Determinant possible values

Q: 3 2. Given A = -1 0 1 0 0 2 1 2 a. Find the determinate of ATA b. Find the determinate for 5A

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Q: [10 0 A = |4 1 0 1 0 1 2 4 0 1 3 0 1 Determine whether or not A is invertible. (Justify your answer)

A: A is invertible

Q: Q1: The determinate of Matrix A is: * 3 -2 A=[1 4 0.5] 2 O (a) 16.5 O (b) 1.5. O (c) 11

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Q: 2 Find the determinant of 1 3 -1 using -2 6 5 a. cofactor expansion about the 1st row b. cofactor…

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Q: 63. Use the determinant to determine whether A= [; ] 1 2 is invertible. If it is invertible, compute…

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Q: Г-1 3 Let A = -2 5 4 . Find the following cofactors: 0 1 -3 (а) А1з (b) A21 (c) A32 (d) A33

A: Given , A=-123-25401-3

Q: [1 Which of the following values of a will make 2 Lo 2 2 a non-invertible? (А) 1

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Q: 4 8. 1 Evaluate the determinant 7 -6 0 3 1 4 8 1 6 0 =-1 %3D - 3 2 1

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Q: Solve all

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Q: 3 4 0 -3 0 k 1 Suppose B = 2 1. 6 0 4 2. 6 a) If k = 1, what is the det(B)? b) What value of k makes…

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Q: 1 1 5 1 2-i + 5i 1+2i oVerify that: (1) (2) 2- 3i +i 26 26 3- 4i 3 i 30 – j19 (3) 21 -1 (4) i (1-J3…

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Q: Compute the determinate by cofactor expansion at each step Choose a row or column that has at least…

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Q: Find the RREF of [A| I], then determine whether A is invertible and, if so, find A-1. 2 -2 1 2 3 (i)…

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Q: [1 3 7 =0 2 5 verildiğine göre Det(-A)+ Det (A 0 2 6 determinant(A) +determinant(inverseA)=? 12:08

A: We will find out the required value.

Q: The determinant of the matrix 4 log 2 sin(33) A = 2 3x2 – 3 102 x2 – 1. is equal to: Select one…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.