Q3) a. If a = i-2j +k, b =i+ 2j-4k , c = 2i -3j + k Evaluate: D= ( a x b )x( a xc) %3D b. Determine the inverse of the following matrix if it is invertible; 3 2 C = 4 1 1 1 2 3

Q: Is this statement true? It is possible for the square matrix A to be invertible and to have its…

A: Note: The determinant of a square matrix A indicates whether A is invertible or not.Now, det(A)=0 if…

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A: consider the matrix of the form abcdefghi consider example 123484265 the inverse of the matrix…

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Suppose that Q is an orthogonal matrix, then O a lQ°| = 4 O b. Q°| = 2 O d. Q°| = 0

A: This question is related to Linear Algebra

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: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

A:

Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

A: Given: The linear system of equations is, The inverse of a matrix is calculated by using the…

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

A: The coefficient matrix is, Now,

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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: a) Factor the matrix A into the product XDX- where D is diagonal. (-1 -2 2 A = 4 3 -4 -2 b) Verify…

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Q: Find inverse of matrix A by Gauss-Jordan me [2 -1 2

A: Here we have to find the inverse of the matrix by the Gauss-Jordan method.  we have,

Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: : Find the inverse of the matrix 1 1 -1 0 -2 1 A = 3 -1 2 with using the method of Cofactor…

A: firstly find cofactor of A and then adjoint and use  A-1 = adjA/|A|

Q: 2 In what direction does f(x) = 7xy - 9x increase most rapidly at (4, - 1)? V f(4, - 1) = (Type an…

A: I am attaching image so that you understand each and every step.

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 5 11 1 6 15…

A:

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: b) Solve the following set of linear equation +2x, +x, = 4 -2x3+3x - 4x, = 2 5x +3x, + 5x, =-1| %3D…

A: The objective is to solve the system of linear equation.

Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Let A=2301-2-120-1 , I=100010001. Combining the matrix A and I to form a augmented matrix. The…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3 -2]…

A: A=13-223001-1

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given: 1514

Q: Show that the matrix is not diagonalizable.

A:

Q: 7. Determine, using matrices, if the following system of equations is dependent. If it is dependent,…

A: Given system of equationx+4y-2z=-32x-y+5x=128x+5y+11z=30 converting above system of equation into…

Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

A:

Q: Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.…

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Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: In what direction does f(x) = 2xy – 7x increase most rapidly at (6, - 2)? %3D V f(6, - 2) = (Type an…

A: Given query is to find the direction of moast repid increament.

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A:

Q: Solve the matrix by using Cramer's Rule method 2x+5y+2z=10 3x+8y+z=3 2y+5z=1

A: To solve the matrix by using cramers rule method.

Q: If A is invertible matrix, then (2AT) %3D (A) 를 (4-1)" (B) 2 (A-1)" (C) 2 (A")-1 (D) 글A-1 (E) AT

A:

Q: Solve the same system using Cramers Rule Augmented Inverse of the coefficient matrix 4x-zy=0 3x+3y=5

A:

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

A:

Q: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: 2- Consider the matrices A = [₁²1], B = [₁ J₁ C=__=₁} K₁ = [50], K₂ = [₁²2] Solve AX + BY = K₁ CX +…

A: Given: The matrices are A=3211 ,B=0110,C=111-1, D=11-14,K1=5000 and K2=21102. To find: The matrixes…

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

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Q: Find the inverse of the matrix and verify that A-!A = AA1- 1. 4--10 A 3D 2. 8. A-1 Show My Work…

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Q: Suppose A=QR, where Q is m×n and R is n× n. Show that if the columns of A are linearly independent,…

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Q: Explain why the columns of an nxn matrix A span R" when A is invertible. Choose the correct answer…

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Q: Suppose AB = AC where B and C are mxn matrices and A is invertible. a.Show B = C. b.Is this true…

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Q: Suppose A = is positive definite matrix then: 10 O a. Ja| V20 O c. la| < 20 O d. a < -V20 2.

A: Since positive symmetric metrix Det(A)&gt;

Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: • The Matrix B from 3 x 2 at b, = -1+; is го 1. 2.

A:

Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

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

A:

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Suppose A, B, and C are three non-zero square matrices such that AC = BC. Is it true that A = B? If…

A: Not true