E. A square matrix 39. Let A be a matrix such that A2 A then, if B A -I then: A. B? = B B. B2 = 2B C. B2 = I D. B2 = -B E. B2 = BI %3D IE LAL IRI

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A: a) A matrix is upper triangular if all the elements below the main diagonal is zero Hence it is not…

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

A:

Q: Let [1 2 [1 A = 2 41 1 3 and B = |2 1 [2 2 6] 2 4] 3 [1 2] Find the elementary matrix, E such that…

A: Two matrices A=124213102 and B=124213226 are given. We have to calculate the matrix E that satisfies…

Q: Is this the correct definition of upper triangular, for a matrix A? Aij * 0 when j 2 i O Yes No

A: Since you have asked multiple questions , we will solve first question for you. If you want any…

Q: If A is a square matrix such that A2 = A, then (I-A)+A is equal to (A) (В) (C) I- A (D) I+ A

A: A is a square matrix such that: A2=A Now: (I-A)3 + A=(I-A)2(I-A)+A =(I2-2AI+A2)(I-A)+A = (I-2A + A)…

Q: Find the matrix A such that 1 0 A -2 -3 -1 3 -1 a b Hint: Let A = c d C A =

A: Given a matrix A -             We have to find-

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 1 4 -5 1 3 -6 4 A= 4 1 -6…

A:

Q: Find a matrix B such that AB = I, where 4 1 1 0 A = and I = -4 4 1 a b Hint: Let B c d B =

A:

Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

A:

Q: Use the given information to find A. A-1 [$3 4 5 5 12 NOTE: Write the elements of the matrix…

A: Topic = Matrix

Q: Use Cayley-Hamilton to calculate eAt for the following matrix:

A: In this question, we need to find the matrix exponential. here we use the application of…

Q: Let A be a 5 x 9 matrix. Which of the following statements is (are) true? Ob and d O c) Nullity of A…

A:

Q: (b) Write down a possible matrix A such that when we apply the above elementary matrices, we get an…

A: Given: The 3 by 3 matrices that produce the elimination steps. E21 subtract 4 times row 1 from row 2…

Q: We call a square matrix E a projection matrix if E² E = ET . If P is an orthogonal and symmetric…

A:

Q: Let A be an n x m matrix. What is the value of rank(A) + nullity(A)? A) т B) n +1 C) m + n D) т — п…

A: given matrix A is of order n*m to find  rank(A) + nullity(A)

Q: For any square matrix A, AAT is a a. Diagonal matrix b. Symmetric matrix O c. Skew symmetric matrix…

A: For any square matrix A to find AAT  is which f the following.

Q: Let A be a nonsingular n × n matrix and let B be an n×r matrix. Show that the reduced row echelon…

A:

Q: If A is n x n matrix and a E N (AT A), then a. IEN (AT) O b. r b. IEC (A") Oc. rEC(A) O d. rEN(A)

A:

Q: Find the matrix E so that EB=C, where |1 a2 az 0 B2 B3 a1 a2 dz B= b, b, b, & C= |C1 C2 C3 with a,+0…

A:

Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

A:

Q: Which of the following is the LU-factorization of the matrix a) 1 b) 0 1 1 c) d)

A:

Q: Let A be a n x n real matrix. If the rank A =n find the following: (a) Col A (b) Nul A (c) nullity A

A:

Q: Given the that if you are Ucurrentty in state E, you will wind up in state B. following matrix find…

A: From the given transition probability matrix, We have probability, Pij = prob(This step Si |Next…

Q: c. Consider the multiplication AB is existing with the size (M x N), where B is a matrix of size (L…

A: Solving Part C only ..as you have already mentioned :-

Q: Find the specified change-of-coordinates matrix. Let B= {b1, b2) and C= {c, c2) be bases for R?,…

A:

Q: Suppose A is an x n matrix. (a) If ker(A) = (b) Give an example of a matrix with ker(A) = im(A).…

A:

Q: [0] Let A = : 1.B = : J.c = 6 1. and V = [1 2 31 l4 5 6 „B = lò ol.c = 6 1, and v = |1. What is the…

A:

Q: 3. Let A be a lower triangular matrix with elements a;j. Then a;; O when %3D O izi O isi O i>j O i<j

A: Let A be a Lower- Triangular Matrix. Then, A=100210431, A is any lower -triangular matrix.

Q: -1.T If A is 3x3 nonsingular matrix such that AA' =A'A and B=A A' then BB' = Select one: (B*," b. в…

A:

Q: For what values of A is the matrix below singular? [λ 9 Lo 9 07 λ 4 4 21

A:

Q: If A is n x n matrix and (I- A)² = I- A then O a. AT = A %3D O b. AT A = I O c. AAT = I Od. A? = A

A: We have to solve given problem:

Q: If A is a 4 x 6 matrix and the dim Nul A​=3, what is dim Col A​?  Justify your answer.

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). -4 0 4 A= 8 3-5 8 12 13 ..…

A: Topic :- matrix algebra

Q: A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E,…

A: A lower triangular matrix of matrix A is  .......

Q: Find an LU factorization of the matrix A (with L unit lower triangular). -5 0 4 A = 15 2 - 9 15 8 8…

A: Given that  The matrix A  To find the LU by using LU factorization

Q: 3. If A and B are 2x2 matrices. Find a matrix C such that: a) C= AT+B B A b) C= LA+1 B+2 c) C=…

A: 3 Given A and B are 2×2 matrices. We have to find the matrix C. Let A=1001 and B=1111. a Given…

Q: O If E is an elementary matrix then so is E". O Let A and B be m x n matrices and D be an n x n…

A: We will prove the given statements.

Q: Find an elementary matrix E that satisfies the stated equations. 8. 1 5 8 5 8. 1 5 B = 2 -7 D -6 21…

A:

Q: Z-Lubrary. The worl. 2 Toyota South Africa The light at the end. The patent profile a a Nwu Vietual…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: b7 c d x A = j g _e f] a If then size of matrix A: %3D

A: Here we find size of Matrix A ?

Q: Find the elementary matrix E such that E A B where | 7 A = -15 -1 and B = 16 16 9. -15

A: The solution is given as

Q: if A is (m*n) matrix, prove 'rank(AB) < max(rank(A), rank(B))' only A: (m*n), B : (n*k)

A:

Q: For a ,b element of real numbers, min{a,b} =a if a≤b and if b ≤a. Let A =(aij) be a 3×3 matrix with…

A: Given that the matrix A is 3×3. The elements in the matrix is defined as follows. aij=max1,i,-j

Q: Use the reduce echelon form "triangle upper matrix" to find the det(A), where A = 2 -8 6 8 3 -9 5 10…

A:

Q: A upper triangular matrix of matrix A is a. U = E, E1... E, E, A b. U = E, E,... E, E A c. U = E,"…

A: An upper triangular matrix of matrix A is can be represent as U = EkEk-1........E2E1A This form is…

Q: Let be A, B, C three matrixes 30 1 B = z A = 2 y C = 5 13 -10, 10 What is the value for X that…

A: We will solve for x.

Q: The trace of an n × n square matrix A is the sum of its diagonal entries, denoted Tr(A) = a11 + a22…

A: Let A=a11a12...a1na21a22...a2n........an1an2.ann and B=[b11b12...b1nb21b22...b2n........bn1bn2.bnn]…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 2 4 - 1 1 4 2 4 A = 4 10 8…

A: We have to write the U matrix using LU decomposition method.

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.