1 1 -2 0 3 -5 -1 2 A = 1 1 2 4 2 1 3 3.

Q: Use properties of determinants to find the value of each determinant if it is known that

A: x yzu vw1 23 = 4   x   y  z-3-6-9   u   v  w = ?

Q: If ∣A∣ = 7 and A is of order 4, then find each determinant.(a) ∣3A∣ (b) ∣AT∣ (c) ∣A−1∣ (d) ∣A3∣

A: Here given Use the property of determinant which states that

Q: Multiply each entry in row 2 of a 3 by 3 determinant by thenumber k, k ≠ 0. Show that the value of…

A: Consider a 3×3 determinant, ∆=a1b1c1a2b2c2a3b3c3   =a1b2c3-b3c2-b1a2c3-a3c2+c1a2b3-a3b2 On…

Q: Use the determinant to decide whether the matrix B given below is singular or nonsingular. B-/14 14…

A:

Q: Use the method of elementary operations to evaluate the determinant 2 -4 3 6. 1 2 -2 3 -5 4 -4 -2 3…

A: To find- Use the method of elementary operations to evaluate the determinant 2-43612-23-54-4-23734…

Q: Use determinants to find x in the below equations: 5x + y - 3z = 0 - 9x + 2y + 5z -1= 0 4x + y -…

A:

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 an n × n matrix A, explain how to find each value. (a) The minor Mij of the entry aij (b) The…

A: (a) To determine: The minor Mij of the entry ai j of the n x n matrix A.

Q: Let a, b and c be constant numbers. Show that 1 1 1 a b C = (b− a)(ca)(c - b) a² b² c² You can only…

A:

Q: Without performing calculations, explain why the determinant of 1 0 0 3 0 4 2 -1 8 3 -2 4 1 is zero.

A: We prove that rows of the matrix is linearly dependent. If rows of a matrix is linearly dependent…

Q: Use determinant to decide if the following vectors are linearly independent: -8 7 -4 -6 7 -5

A: We know that the vectors {v1, v2, v3} are linearly independent  if det( v1, v2, v3 ) ≠0 Where…

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

A: The second order determinant means the matrix is order 2×2 . Consider a matrix A=abcd . This matrix…