theorem. An example of proof can be seen in the picture, maybe it can help you Theorem The determinant of a matrix A of size n x n can be calculated by multiplying the entries in a row (or column) by their cofactors and adding the resulting product; that is, for every 1≤ i ≤ n and 1 ≤ j ≤ n then det(A) = a1jC1j + a2jC2j +... anjCnj   (expansion of cofactor along column j) and det(A) = ai1Ci1 + ai2Ci2 +... ain Cin (cofactor expansion along row i)

Q: 2a₁b₁ Let A ab₂+ a₂b₁ ab3 + a3b₁ a₁b₂+ a₂b₁ 2a₂b2 a3b₂+ a₂b3 b3 +3₁ a2b3 + a3b₂. Expressing 2a3b3 A…

A:

Q: 26. Let A and B be (2x2) matrices. Prove or find a coun- terexample for this statement: (A - B)(A +…

A:

Q: )| -3,3 2 9 -3 = 2 = 2(1) || 0 0 0 = 2 2( expand along C₁ 0 21 0 = 20 -1 N -4 1 5 3 1 -2 1 4 2 x 7…

A:

Q: 2a₂b₁ Let A = ab₂ + a₂b₁ a₁b3 + a3b₁ a₁b₂+ a₂b₁ 2a₂b₂ a3b₂+ a₂b3 a₁b3 +azb a₂b3+a3b₂. Expressing…

A:

Q: Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or…

A: We will find out the required solution.

Q: -1 1 1 A = ( ). 3 2i В — y 2 -2 -2.

A:

Q: A and B are n x n invertible matrices, then the equality (A +B) (A – B) = A? – B? always true.

A: No this false ,

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A:

Q: You need to provide details/explanations of your solutions, indicate any formulas you are using, and…

A: Step 1: Step 2: Step 3: Step 4:

Q: Given the matrix 3-40000 10 5-300 000 0050000 000-10000 00002-30 000005 4 00004 2 3 Find the…

A:

Q: TRUE OR FALSE? A. If AX=0 has a nonzero solution, the determinant of A is not zero. B. Suppose A…

A: Given, A. If AX=0 has a nonzero solution, the determinant of A is not zero. B. Suppose A is a 10x10…

Q: Find the determinants of the given matrix below. 7 4 9 -2 12 −1 2 5 -4 7 3 -91 4 5 31

A:

Q: must solve all parts for upvote

A:

Q: is                         . B. Suppose the only solution of AX=B is the zero matrix ( A is nxn and…

A:

Q: Use row operations to find the determinant of A = show all your steps.) 4 2 3 1 2 1 1 1 0032 10 1 0,…

A:

Q: Compute the determinant of the matrix. Show all your work including which row operations and…

A: To find the determinant of the matrix we will use the row operations and cofactor expansions.Note:…

Q: This semester you have learnt how to solve simultaneous equations algebraically. Another method of…

A:

Q: a? b? +c² 2 b? c² +a? %3D c? a² +b? 2 S

A:

Q: So  I will give you a matrix. For that matrix find the determinant and show  that the matrix is…

A: The given matrix is .We need to find the determinant and identify whether it is invertible or not.If…

Q: nsider the matrices A = B = 2 C = c- (1 ² 3) 64 69 (a) Calculate AB, BA, AC, BC and (A + B)C. (b)…

A:

Q: a1 bị C1 b2 c2 is given by az b2 The determinant of a 3 x 3 matrix A = | a2 bs CзJ |A| = a1 + az a2

A:

Q: Find the determinant -21 3 24 -3 of the matrix. 0 3 9 -6 6

A:

Q: Consider a 2x2-dimensional matrix A for which A² = -A. a) What are all possible values of the…

A:

Q: So  I will give you a matrix. For that matrix find the determinant and show or prove that the matrix…

A: The objective of this question is to determine whether a given matrix is invertible or not. If it is…

Q: Consider the NxN-dimensional matrices A and B, where B=S¹AS (with S an NXN-dimensional non- singular…

A:

Q: a. a d g -3b - 3e -3h b c e f h i -a b. -d -g 3c + x b 3f+y e 3i+z h

A:

Q: + [12 1 Let A-3-1 2 [101] Find the cofactor matrix C and the inverse matrix A¹. Show the details of…

A:

Q: Compute the determinant of the matrix -1 2) 1 0 0 -1 -1 1 and find its inverse if it is invertible.

A: