Determine the rank and nullity of the matrix 2 1 -1 2 4 -2 A = Note: Rank(A) = dim(A); %3D Nullity(A) = dim(Null(A)). (a) rank(A) = 3; nullity(A) = 0 nullity(A) = 3 (b) rank(A) = 0; (c) rank(A) = 1; nullity(A) = 1 %3D %3D %3D (d) rank(A) = 1; nullity(A) = 2 nullity(A) = 1 (e) rank(A) = 2; (f) rank(A) = 2; nullity(A) = 2 %D %3D %3D

Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

A:

Q: 3) Consider the following matrix: A= 220 001 0 10 - 1 1 (i) Compute A™ ¹. (ii) Write A as a product…

A:

Q: why is the matrix like that?

A:

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

A:

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Find the rank of the matrix A = 0 1 16 14 -3 1

A: Note:To find the rank of a matrix, transform the matrix into its echelon form. Then, find the rank…

Q: (1) Let A and B be two 2 × 2 matrices. Does det(A – B) = det(A) – det(B), explain your answer.

A:

Q: Illustrate the Skew-symmetric matrix ?

A:

Q: Describe and compare the solution sets of x₁ + 4x2 - 7x3 = 0 and X₁ + 4x2 - 7x3 = -6. X₁ Describe…

A:

Q: Find the matrix A if 2 1 A = 4 2 %3D -1 3 1 3 B3: A =

A:

Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: -1 3 -12 0 5 -2 -1 ^- |- Determine whether A is diagonalizable. late (4)10 If A is diagonalizable,…

A:

Q: Give the rank and the nullity of the matrix. A = rank(A) = [ nullity (4) = [ 30-3 22 2

A: