If A and B are arbitrary real m × n matrices, then the mapping (А, В) trace(A" в) efines an inner product in IR"X". Use this inner product to find (A, B), the norms ||A|| and ||B||, and the angle a 4.B between A and B for 3 -3 1 -3 A = -3 3 and B= -2 -1 1

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

A:

Q: Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x.…

A:

Q: In linear algebra, if a vector is in the range of a matrix A, then it is also in the null space of…

A: The given statement is False.

Q: Suppose that matrix A has dimension 5•3 and that matrix B has dimension 3•5. Decide whether product…

A: Given: The matrix A has dimension 5×3 and that matrix B has dimension 3×5. To Find: To decide…

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

A:

Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

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

A:

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: 0 5 Let A= 4. diagonalizable matrix( A-XDX), then X and D are: 1 Select one: a. -5 X= -5 0 4 0. b.…

A:

Q: -1 find its inverse A¬'. Check that your inverse is actual in 2 For a matrix A = -3 Ichow vour work…

A:

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

A:

Q: If the RREF of All is || B, then AB is the identity matrix. A) True B False

A: Given: The row reduces echelon form is A:I is I:B. We have to check whether AB is the identity…

Q: Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the…

A: Let T be a 2x2 matrix given as T = abcd.Let the line be given by y = mx+c.Any point on the line can…

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

A:

Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

A:

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: A diagonal matrix is a square matrix that if rotated to give the original matrix 1- right 2-Error

A: a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term…

Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

A:

Q: The matrix X1 X = is called a vector.

A: We have to find

Q: Is the following matrix diagonalizable¹? 3 B=0 0 -3 1] 3 1 0 3

A:

Q: Let A be a 2 X 3 matrix, B be a 3 X 2 matrix and v be a 3 X 1 vector. Indicate the dimensions of the…

A:

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: IA - (34) and B- (-5 8 -2 (a) (AB) (b) BTAT 10. f -5 find

A:

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

A:

Q: Let A and B be n × n matrices and assume that columns of B are linearly dependent. Show that columns…

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.