An inner product for M2,2 matrices {A= ao, a1, a2, a3 ER} is defined as %3D a2 a3 < A, B >= aobo + aibı + 2a2b2 + 3azb3. Using A= and B= -2] answer the following questions. Al. Calculate the determinant |2B3). B Calculate ||A|| = V< A, A >. 7 Çalculate ||B||-

Q: Let A and B be square matrices of order 3 such that JA| = 4 and |B| = 9. (a) Find AB|. (b) Find…

A:

Q: Let A and B be 3x3 matrices, with det A = - 7 and det B = 7. Use properties of determinants to…

A: To Determine: compute detAB=-49 Given: Let A and B be 3×3 matrices with det A=-7  and det B=7…

Q: Compute the determinant of A by by transforming the matrix into a triangular matrix. A = 3. -1 -3 4…

A:

Q: Let M be a 10 × 10 real matrix such that M2 = M and the determinant of the matrix cannot be 1. Does…

A:

Q: Find the determinant of the given matrix using the following method: 1.3 Property 11 1.3.1 Choose 3…

A:

Q: Let A 2x2 matrix. A satisfies with tr (A² ) = 5 and tr ( A) = 3. Find determinant of A.

A: Use property of eigen value

Q: Suppose AB = AC, where B and C are nxp matrices and A is invertible. Show that B = C. Is this true,…

A: Given that AB=AC  and  A is invertible. Therefore, A-1 exist. This implies that,…

Q: Show that 4 is the largest determinant for a 3 by 3 matrix of 1 'sand -1 's.

A: To show: 4 is the largest determinant for a 3 by 3 matrix of 1 'sand -1 's.

Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: Compute the determinant of the matrix using the best possible method. Zmatrix ((2 -2 6 4)(2 3 7 1)(6…

A:

Q: Let A and B be n × n matrices and let C = AB. Use determinants to show that if either A or B is…

A: Given :-  A and B  be n x n matrices  and  C = AB Singular matrices :-  A matrices singular when…

Q: Use the method demonstrated in Example 5 to find the determinant of the matrix. 6 -8 0 -7 4 1 5 3.

A:

Q: 1.What is the definition of the cross product?2. How is the determinant of a 3 × 3 matrix used in…

A:

Q: Let a2 az A = | b1 b2 b3 C1 C2 C3 Suppose that det(A) = 3. Find the determinant of the following…

A: On changing determinant of row to corresponding column, there will be no any change on…

Q: Find the area of the triangle with vertices (1, 0), (2, 2), and (4, 3)

A:

Q: Compute the determinants of the follow- ing matrices. 3 2

A: The solution is given as follows :

Q: :what is the determinant of the following matrix 3 0 0 107 1 0 V2 2 6

A: We have to find the determinant of the matrix 30010710226.

Q: Linear algebra

A:

Q: -1 1 2 1 2 3 1 2 3 -1 2 3

A: Given lower triangular matrix :100⋯0120⋯0123⋯0123⋱0123⋯n

Q: If P is an invertible n × n matrix, show that: det(P−1A2P) = (det A)2 using the determinant…

A:

Q: Use the cofactor expansion theorem to evaluate the given determinant along the specified row or…

A:

Q: Compute the determinant of A by using a cofactor expansion: [8 6] 3 l3 -2 5] 1 A = |4

A: find the determinant using the first row

Q: Consider a 4 x 4 matrix A with rows vi, v2, v3, and v4. If det(A) = 5, find the determinant of the…

A:

Q: Let A = [a1, a2, a3] be a 3 x 3 matrix whose columns are a1, a2, a3 and whose determinant is detA =…

A:

Q: Consider the matrix. x 55 K = 0 27 46 ,x € R 0 65 84 40 If we know that |K| is different from zero,…

A: The determinant of a lower triangular matrix (or an upper triangular matrix) is the product of the…

Q: Compute the determinant of the tollowing matrix using a cofactor expansion acro 56 -6 4 0 6

A:

Q: The volume of a parallelepiped having A, B and C as edges can be obtained by finding the determinant…

A:

Q: Consider the following system of linear equations: 2x, +2х, — х, %3 6 4х, +3x, + х, %319 1. Зх, —…

A:

Q: TRUE/FALSE Assume that all the given matrices are n × n. If A and B are row equivalent matrices,…

A: Given: All the given matrices are n × n. A and B are row equivalent matrices.

Q: Let A is an orthogonal matrix, that is, AAT = I and B? = I. Compute the determinanm of the matrix…

A:

Q: Let M be a 10 x 10 real matrix such that M² = M and the determinant of the matrix cannot be 1. Does…

A:

Q: Q3: (a) Compute minors (M11, M12 „M13 ), cofactors (C11 , C12 , C13) and find determinant of the…

A: To find a determinant with the reduction method, we have to reduce the given matrix as follows: (1)…

Q: 4. Evaluate the determinant of the matrix by using a convenient column or row. (a) 3 -1 3 1 A = 2 0…

A:

Q: Write down a n × n matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.

A: claim- write down a n×n matrix A such that CondA=1, but detA→0 as n→∞. it is known that condition…

Q: Suppose C is a 4 x4 matrix such that det (C) = 3. What is the determinant of the matrix B=2C?CIc-1?…

A: Given :det(C)=3C=4×4 matrics

Q: Let a2 аз A = | b1 b2 bz C1 C2 C3 Suppose that det(A) = 5. Find the determinant of the following…

A:

Q: Suppose AB = AC, where B and C are nxp matrices and A is invertible. Show that B = C. Is this true,…

A: Given information: Consider AB=AC and B and C are n×p matrices and A is invertible.  Calculation:…

Q: Q3: (a) Compute minors (M21, M22, M23 ) , cofactors (C21 , C22, Cz3) and find determinant of the…

A:

Q: By calculating AB and evaluating the determinants, verify that det AB = det A det B a12 b12 for the…

A:

Q: 2. For the matrix A given in #1, compute the determinant using LU factorization.

A:

Q: 4. Evaluate the determinant of the matrix by using a convenient column or row. (a) -1 3 0 0 1 0 3 1…

A:

Q: Expand the determinant of B by the second column and evaluate the occuring algebraic subdeterminants…

A:

Q: Suppose A, B are 3x3 matrices, det A = 6, and det B = -5. Find the following determinants. (a): det…

A:

Q: (b) Given that A and B are 3x3 matrices where det(A) = -3 and det(B) = 3. Compute the following…

A: solution:Given A and B are 3×3 matrices .Also, det(A)=-3 and det (B)=3.WE need to find detA2T.(2B)-1…

Q: Use the method demonstrated in Example 5 to find the determinant of the matrix. 3 8 -7 0 -9 4 8 1 5

A:

Q: [1]a- Prove that a square matrix A is invertible iff A"A is invertible . b- Prove that without…

A:

Q: Suppose AB = AC, where B and C are nxp matrices and Ais invertible. Show that B= C. Is this true, in…

A:

Q: Consider a 3 × 3-matrix whose first row is a vector a, the second row is a vector b, and the third…

A: given row  of  3×3  matrix  is          a   , vector      b   , vector c=2a+3b    , vector

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.