49. The product of 2 × 2 matrices A and B is the matrix AB defined by (:)(:)- a' b' d d' aa' + bc' ab' + bd' ca' + dc' cb' + dd' a b d B AB The (i, j)-entry of A is the dot product of the ith row of A and the jth column of B. Prove that det(AB) = det(A) det(B).

Q: If the matrix A has orthonormal columns, then AAT = I %3D

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Q: Suppose that 60% of the people who own a GM car buy a GM car for their next vehicle. Also, suppose…

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Q: Show that if (x)is a solution of y'- AY where A is 2x2 matrix of real ombers then d = AÐ %3D Maximum…

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Q: 1 3 14. For the vector b=b, to be in the row space of the matrix A= then 256 by . by-4bz +1 lb, = 0…

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Q: f A is 3×3 nonsingular matrix such that AAT=ATA and B=A-1AT then BBT=

A: Given that: A is 3x3 non singular matrix and AAT=ATA and B=A-1AT

Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: e/ By three ways Show that B= %3D isorthogunal matrix

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Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

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Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

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Q: Suppose z" Ar = r}+10x122+ 25x where a = then %3D O a. A is indefinite matrix Ob. A is negative…

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Q: Find a 3 × 1 matrix x with entries not all zero such that

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Q: Suppose A is a matrix that reduces after elimination to 1 2 3 0 R 0 1 1 0 0 0 0 1 The rank of A is…

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: Suppose that collA) = IR+ 4x7 matrix A has 4 lead terms Then and NCA) = R³ %3D %3D

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Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

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Q: 4 It is known that the system Ax = b is consistent, where A E Mmxn. Define a matrix BE Mmx(n+1) as B…

A: A matrix Ax=b  and A is a column matrix then A is consistent iff b can be written in the linear…

Q: With each m xn matrix Y we associate the column vector vec(Y) of length m x n defined by vec(Y) :=…

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Q: Suppose A is ann x n invertible unit lower triangular matrix and n » 10. A programmer claims that as…

A: We will use the basic knowledge of LU decomposition to answer this question.

Q: How many rows and columns must a matrix have in order to define a mapping from R5 into R7 by the…

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Q: Given A = 1 1 0 3 Compute 5A *Matrix

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Q: 5. If xy + 2xu + 3xv + uv-| = 0, 2xy + 3yu – 2xv + 2uv + 2 = 0, ſind the Jacobian matrix [ ].

A: Let, F(u,v,x,y)=xy+2xv+3xv+uv-1Gu,v,x,y=2xy+3yu-2xv+2uv+2 By the chain rule,…

Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

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Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

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Q: Compute the matrix exponential e At for the system x' = Ax given below. x²₁ = 20x₁ − 20x₂, x′2 =…

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Q: (b) By replacing A with another matrix B different from A in only a single entry, define an inner…

A: To prove a function to be an inner product, we have to show it satisfies the following five…

Q: Го 6. Show that the matrix does not have an LU decomposition by considering the product [l11 0 [121…

A: Given :0110

Q: Suppose AB = C, where A and C are upper triangular. (a) Find 2 × 2 nonzero matrices A, B, C, where B…

A: Answer

Q: [13 5 matrisinin rankının 2 olabilmesi için c aşağıdakilerden hangisi olamaz? 26 c if the given…

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Q: 2. Q is an xn symmetric matrix, b is a vector of size n and c is a scalar If f(x) = x"Qx + b"x + c:…

A: given  fx=12xTQx+bTx+c it is known that  gradient of the function can be expressed as…

Q: (a) What is the 2 × 2 matrix P that projects v = x y onto the x axis, i.e. takes x y to x 0 ? Is P…

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Q: 6. To identify 3 x 3 matrix Abr fis positive definite if and only if cfr r> 0, r²- ab >0 and 4>0. O…

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Q: The size of the matrix X'Y, where X is a design matrix of size (k+1) by (k+1) and Y is the vector of…

A: The size of design matrix X is given by (k + 1) by (k + 1)  And Y is the vector of values of…

Q: O If A is possi ble value of dim Nul AT ? Please explain an 8x 5 matrix, what is

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Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: а? а.b а. с a? ab cos y ac cos B = b. a b? b.c = ab cos y bc cos a С.а с.b с? ас cos B bc cosa =…

A: Consider the given matrix :A=a2a.ba.cb.ab2b.cc.ac.bc2   =a2ab cosγac cosβabcosγb2bc cosαac cosβbc…

Q: 16 - х For what value of x, 13. 47 is a singular matrix: - A. 1 В. 2 С. -1 D. -2 E. None of the…

A: A matrix A is said to be singular if its determinant is zero .

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

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Q: [2 3 find the invers of matrix A by using the elementary row operation, where A = 5.

A: For finding the inverse of any matrix A, at first we augment it with an identity matrix on the…

Q: Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by…

A: (a) The 4 x 4 matrix equation relating the column vectors f and x will be:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then O a. QQT = I O b. QQ" + I Oc Q" = Q1 O…

A: Given Q is a 3×2 matrix then QT is a 2×3 matrix.

Q: 4 For A= calculate A by using Adjoint Matrix Method. (Do not use any other method) 3 5

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Q: Show that the condition number of the square matrix, X (generated with X;j = 461-2), grows i+6j–2 as…

A: We will use the conventional definition of condition number of a matrix.

Q: In this problem you will solve the nonhomogeneous system 5 A. Write a fundamental matrix for the…

A: Here, Ψ-1=-sin3t34sin3t+3cos3t15cos3t33sin3t-4cos3t15g(t)=-14

Q: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: solve for matrix Colfficients A. CCX=l,y=l-),2=0]] 3.CCx=1,y=1,2 =]] CCa--4),-(-1をこ0 CCX=3,y=3,=)…

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Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then O a. QQT = I O b. QQT + I OCQT = Q1 Od.…

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Q: The aim of elimination steps in Gauss elimination method is to reduce the coefficient matrix to a)…

A: A matrix where the number of rows is equal to the number of columns is said to be a square matrix…