a) Given the following matrices a = -and c= nd 2. 3 and C = 2. i) AT C. i) 2(BC"). i) D if (2AB)" = D. %3D

Q: Let B and C be n×n matrices with the property that Bx = Cx for all x ∈ Rn. Show that B = C.

A:

Q: ix A, find (if possible) a nonsingular matrix P such that P-AP -3 0 0. 15-4 4 0 5

A: Introduction: A square matrix A is diagonalizable in linear algebra if it is similar to a diagonal…

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 A and B be 2x2 matrices such that B is invertible If detA)2 and det)-, then detA'e) Select one:…

A:

Q: Which of the following matrices is elementary matrix? To 31 liol a. C. [2 01 d. [2 b.

A: Since your question has multiple subparts we have solved the first three subparts for you.  Identify…

Q: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

Q: Find the matrix D such that ADB = C and hence evaluate f(D-1) given that 4 -2 3 1 6. -6 6:2), c = (6…

A: d2+4d4=6⇒2d4+4d4=6   (d2=2d4)=6d4=6⇒d4=1⇒d2=22d2+8d3=8*2…

Q: Q2: Let A, B be matrices of size 3x3 such that and AB = A+2I A = -101 21 2 find A, B?

A:

Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 14 x 7 matrix. Then = D Check Answer

A: Given that T: R^b to R^a is defined by T(x) ° Mx and M us 14 × 7 matrix.

Q: snip

A: Given, A=abcdD=ad-bc≠0

Q: If A is any matrix, to what is tr (AA T) equal?

A: Let A=[aij] be n X n matrix. Then  AT=[a'ij] where a'ij=aji Let C=AAT=[cij] , where

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

A:

Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 24 x 19 matrix. Then %3D a = b =

A: If T: from Rb to Ra then M is always a×b matrix.

Q: Let A = ; 1.B - : J.c= , ], anc 2 37 ol.c = [ 1 and v = |1. What is the sum of the entries of the L4…

A: Note: We know that for matrix P of order m*n and Q of order n*t, the multiplication PQ is possible…

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

Q: Find the triangular factorization A = LU for the matrix A = 1  1  6      -1  2  9       1  -2  3…

A: Given       A=116-1291-23

Q: If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x =…

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: Q/ A seume where I .4.3 A = and yasaxニメ+I 3. unit Matrix, Find YCA) ? is 526

A: Solution: The objective is to find y(A)

Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

A:

Q: and that h(T) = T² – 2T – 7, find h(A). The questions should read as attached. Change made at the…

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

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

A:

Q: Suppose A= #B+C where B is symmetric and C is skew-symmetric matrices, 56 B = b12 then byn %3D O a.…

A:

Q: Q/ Let A: am et fox)= 2x- 子 4x+5 whene I Find FCA) is unit matrix

A:

Q: Let D = P'AP be a diagonal matrix, wher %3D Pesell thet if D:

A: Given, D=P-1AP be a diagonal matrix, where P is an orthogonal matrix. To prove that A is symmetric.

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

A: x+y=1 x-y=2 We need to find the inverse using A-1 =(1/detA)adj A

Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

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: Consider the ordered bases B = {1+x, 1 – x} and B' = {u1, U2} for P1(IR), and suppose that 2 Q = ( -…

A:

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

A:

Q: Given the bases B={u , U2} and B' ={u'1, u'2} for R2, where and u'1= u' 2 U2 from B to B' is: The…

A:

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: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: Let A be an m×n matrix, X an n×r matrix, and B an m × r matrix. Show that AX = B if and only if Axj…

A:

Q: (4) Given matrix A = G ). and that h(T) = T² – 2T – 7, find h(T).

A:

Q: Consider the matrices A = 1B = ; J, c = ; =G [5 2 K, = l, K2 =L0 3 Solve AX + BY = K, CX + DY = K,…

A: Given matrices A , B , C and D. Matrix K1 and K2 are also given. We need to find matrices X and Y.…

Q: Given C and D are matrixes, and their products CD and DC exist, what can we tell about their…

A: Matrix multiplication is the process of multiplying two matrices using dot product. Dimension of 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 A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

A:

Q: [1 Let A = 2 and V = |1]. What is the sum of the entries of the B = %3D 14 5 1 matrix VT (AT — (А -…

A: We have to find sum of entries of given expression.

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

A:

Q: [1 0 2 31 l4 5 B = 6 ol,c = l6 ál, and V = |1|. What is the sum of the entries of the Lo. matrix VT…

A:

Q: Find all possible choices of c that would make the following matrix singular:

A: For a singular matrix, the determinant value has to be equal to 0. |A| = 0

Q: W is a 120 x 60 weight matrix, What are the dimensions of dW? According to the principle of…

A: Given that W is a 120×60 weight matrix. We have to find the dimension of dW Since, we know that…

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

A: Given det(A) = 6