1. A matrix is symmetric if for each pair of indices i and j, the i, j entry equals the j, i entry. A matrix is antisymmetric if each i, j entry is the negative of the j, i entry. (a)Give a symmetric 2 x 2 matrix and an antisymmetric 2 x 2 matrix. (b)Show the set of all the symmetric 2 x 2 matrices is a linear space(denote SR²X2); (c) Give a basis of SR2x2 and the dim(SR²x2).

Q: Let A = x-2 3 1 x-4 3 2 x-6x3 For which values of r a) the matrix has no inverse, b) its columns are…

A:

Q: Find u and usuch that the null space for the matrix U= 3 v= 0 -2 1 1 -3 -15 1 - 9 1 is span{u, }.

A:

Q: Verify that if r < s, then rows rand s of a matrix can be interchanged by performing 2(s - r) - 1…

A:

Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

A:

Q: (b) B={(-1,3), (2, -1)} and 8' = {(0, 10), (5,0)} (c) B={(2,5), (-1, -3)} and 3' = {e1, e2} (d)…

A:

Q: Find a real symmetric matrix. Q=xC_x_ such that where a) Q = x₁² + 2X₁ X₂ +3 x ²³² + 6 X₂ X ₂ +…

A: We have given a quadratic form .and We have to find the real symmetric matrix..

Q: The maximum value of the determinant among all 2×2 real symmetric matrices with trace 16 is

A: But they cannot be both negative as a+d=16 And the value of ad is maximum  a=8, b=8 Therefore

Q: Describe all matrices which satisfy det(-A) = -det(A).

A: Assume a square matrix A of order n

Q: Construct the augmented matrix

A: We first write the given equations in standard form

Q: 6. In this question show all linear systems resulting from your work, their augmented matrices and…

A:

Q: Let A be a 2 by 7 matrix. Then -A is aby_matrix, and A is a-by-matrix.

A:

Q: a) Given the matrices A = = i) A-¹. ii) BT if (3AB) = C. = (₁ 2). Find 1 (¹₁3) and C= 3 3 b) If S³R…

A:

Q: Write a program that does the following: 1) Use the “ones" and the "eye" inbuilt functions to create…

A: Note: Since you have posted multiple independent questions, according to our policy we are only…

Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

A:

Q: Can we use cofactor expansion in a 2 x 2 matrix

A:

Q: v that the matrix is invertible and find inverse of the

A:

Q: : 21 = |-1/v2 1/V2-1 1/V2 1/V2]1 o 01-1/v2 1/V2 31[ 1/V2 1/v2] Given the diagonalized matrix A =…

A:

Q: Let A be a 3 x 3 matrix given by A 1 -1 5 -4 -8 5 7 a) using row operations transform A into an…

A:

Q: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

A: We need to solve the determinant and find the value of x.  Now, if we have a 3×3 matrix…

Q: a) Compute the adjugate of the given matrix A and then compute the inverse of the matrix 1 0 2 A = 4…

A: We have to find the adjugate of the matrix A. We know that the adjugate is the synonym of the…

Q: 0 -1 and whose nullspace Construct a matrix whose column space contains 2 and 522 2 ] contains

A: Explanation is given below:Explanation:

Q: 3. Find all matrices A such that: 936 3 5 4 6 4 6 b) AT A = 81₂ + A² c) (B-¹(AC))¹ = 5(C-¹B) where…

A: With the given condition we will try to find the Matrix.

Q: USE THE SAME MATRIX "E" from above. Verify E x inv(E) is a 4 x 4 Identity Matrix. Fill Up the Empty…

A:

Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

Q: 5. Show that a complex square matrix is unitary if and only if it is unitarily equivalent to a…

A:

Q: Using only these numbers ( 2,1,9 ) as coefficients, create a matrix of size 5x5 (with all…

A: