Let A be a 4 x 4 matrix with det (A) = 1. What is det(2A)? a) 1 b) 2 c) 4 d) 8 e) 16

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: - ; Let A be a square matrix such that A? – 7A+ 81 = 0 (where I and 0 are the identity and zero…

A:

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

A:

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

A:

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: Let E and F be n × n elementary matrices and let C = EF. Is C nonsingular? Explain.

A: Let E and F are elementary matrices and let

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: snip

A: Given, A=abcdD=ad-bc≠0

Q: 2. Show that if A is an n x n real symmetric matrix then (Ax) y = x (Ay) for all x, y E R".

A:

Q: Let A be an m×n matrix. Explain why the followingare true. Any vector b ∈ Rm can be uniquely written…

A: For  matrix A, N(A) is the null space of A. R(A) is the column space of the matrix A and R(AT) is…

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

A:

Q: let A nonsingular matrix, c #0, c scalar (cA)" = CA -1 -1 %3D Select one: True O False

A:

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

A:

Q: b) Prove: Let A be an m × n matrix, R" = NS(A) RS(A).

A: Given: Let A be an m×n matrix , Rn=NSA⊕RSA

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

A:

Q: Prove that B is row equivalent to A if and only if there exists a nonsingular matrix M such that B =…

A:

Q: Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).

A: The objective is to prove that

Q: b) Prove: Let A be an m x n matrix, R" = NS(A) + RS(A). %3D

A: A be an m×n matrix, we have to prove that ℝn=NSA⊕RSA  …1.

Q: Let A be an nxn matrix. If A-= det A adj A is computed, what should AA be equal to in order to…

A: Using the given matrix equation we need to find the value of AA-1 .

Q: 1. Let A = [a;j]4x5, B = [bij]4x5; C = [cij]5x2; D = [d:j]4x2, and E which of the following matrix…

A: Matrix addition: Let A be an m×n matrix and B be an also m×n matrix. A= {aij: 1≤i≤m ; 1≤j≤n} and B=…

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

A:

Q: let B- 8. find a triangel ar matrix A such that

A: A triangular matrix is a type of square matrix. These are of two types:  Lower triangular  upper…

Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+ 1). Which of the following is the matrix A?

A: A be a 2×3 matrix. This means A2×3 . entries of matrix A are ai,j=(i-1)(j+1)

Q: (a) Let M be a square matrix such that M² = 0. Let t, c be scalars and c‡0. Show that

A: We shall solve first question only as you have asked more than one different question - for others…

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

A:

Q: Let A = [aij] be a square matrix If B is obtained by adding a multiple of one row (column) of A to…

A:

Q: Let Mı5(IR) = {A/A and 15th order square matrix with real elements} and consider the linear…

A:

Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find h and k, consistent: which makes matrix t. 6ud Sua = k |

A:

Q: 16. Prove that for any square matrix A, ||A||ž E ||A* A||2.

A: Given: A is a square matrix.

Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

A:

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" Rm be defined by 0-0 x2 x2 f = A

A: To find the derivative of f given: matrix A which has m rows and n columns  also the function f…

Q: Given the cofactor of matrix A, What is the adjoint of A?

A: Adjoint matrix is the transpose of cofactor matrix.

Q: Let the entries of a matrix A = \aij be defined as aij 2i2 – i+j+ g(j), where g is a %3D function of…

A: Given Ais a symmetric matrix therefore aij=aji…

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

A:

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: Let A be a mxn matrix that n > m (a) Explain why A = 0 has at least a non-trivial solution. %3D

A: (a) Given that A is an m×n matrix. The objective is to explain why Ax=0has non trivial solution.…

Q: Let A, Band C be square matrices Such that AB = AC, If A#0,then B-C. 1s this True or false? Explain…

A: Let A, B, and C be square matrices such that AB=AC. If A≠0 , then B=C. Determine true or false.

Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

A:

Q: a b Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A:

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

A:

Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

A:

Q: Let A be a 6 x 5 matrix. What must a and b be in order to define T : Rª → R* by T(x) = Ax? II

A:

Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

A: In a diagonally dominant square matrix, the magnitude of the element corresponding to the diagonal,…