Let P be a 6x3 matrix and Q be a 3x6 matrix. Also, let A and B be linear functions A(x)=P(x) and B(y)=Q(y), where x,y are vectors. Fill in the blanks of the question below and explain your answers. 1. A is a function from Rs to Rt, where s=____ and t=____. The matrix of the composition BA equals ____. The null space of P is a subspace of Ra, where a=____. The range of P is a subspace of Rb where b=____.

Q: Find the specified change-of-coordinates matrix. Let B = {b₁,b2} and C = {₁, 2} be bases for Ⓡ²,…

A:

Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = (0.375,…

A: Given: In this problem, the given details are We want to create a matrix that reflects around a line…

Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

A:

Q: Find the matrix of T(x, y, z) = (3x, -6y) relative to the standard bases. T = Use this matrix to…

A:

Q: Find the matrix A if 3 1 4 A = 11 00

A:

Q: REI [1.5 5 -151 2 30 -1 2 1 .5 and C= [-2]. -.5 16. For this problem, let A = a) Use your calculator…

A:

Q: mark each statement True or False (T/F). Justify each answer.6. (T/F) The echelon form of a matrix…

A: It is a false statement that the echelon form of a matrix is not unique.

Q: Let A and B be two square matrices of order n over a fiéid F and AEF Then (I) tr (AA)=d Ir A; (2) Ir…

A:

Q: X = 4 1 -3 0 0 6 1 2 -12 10 -1 = [X₁ 5 X2 X3 X4]

A:

Q: QUESTION 1 An organization has four departments: A with 680 employees, B with 830 employees, C with…

A: Given, An organization has four departments: A with 680 employees, B with 830 employees, C with…

Q: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: f = -x² - y² + 2xy. Diagonalize the quadratic form, i.e., find an orthogonal matrix P such that the…

A:

Q: het H be a Hilbert space. Consider A, B & BL(H) Prove that || A* || = || A|| and | A²A|| = ||A||²2 =…

A: Let H be a Hilbert space. Consider A,B∈BLH To prove : A*=A  and A*A=A2=AA*

Q: Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a…

A:

Q: (d) Let A be a 4 × 5 matrix. Then the column vectors of A are linearly dependent. True False…

A:

Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: Let A = [ 3*0 .8 = [ Jand C = [14-0 Jand c = [1* | Find the matrix X, if 8+0 -10 A? + 3X =C |B|

A:

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

A: Now the transpose is,

Q: v = (5, 2, -12, 13, 6) u, = (1. 2. -3. 4. -1)

A: Given,              v=5, 2, -12, 13, 6u1=1, 2, -3, 4, -1u2=1, 2, 0, 2, 1u3=0, 1, 1, 1, -4u4=2, 1,…

Q: 3 Construct a 3 x 3 nonzero matrix A such that the vector 2 is a solution of Ax = 0. A = [(1,2,3),…

A:

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 4 - 2 7 -3 + X2 - 9 5…

A: Given vector equation- x13-501+x24-3-99+x3-267-6=7198 To write the vector equation in matrix…

Q: 0 1 1 1 0 3 and B = 100 1 20 0 (a) Solve the following equation for X: BAXA - B (b) You should have…

A:

Q: X = 4 0 1 0 -3 6 1 2 -12 10 -1 = [X₁ X₂ X3 X4] 5

A: Linear algebra

Q: Find the standard matrix of the linear transformation. -y x + 4y бх — 2у

A:

Q: 1. Find A¹ using elementary row operation to the augmented matrix Let A = -2 2 10 0 0 4 2 -6 -12

A:

Q: please show all work 3. Consider the following matrix: B =  (a) Does this matrix have an…

A:

Q: Consider the matrix A == ((1, 2, 5)|(4, 6, 7)|(1, 5, 1)) and the row vector v = > A = ((1, 2, 5)|…

A: As per guidelines, I can do only first question (Question 1.)

Q: Find the value(s) of x for which the matrix has linearly dependent columns 1 -5 -1 -1 -5 7 3 1 8

A: Given matrix 1-5-1-1-57x31

Q: Matrix  A = a11 a12 a21 a22 a31 a32 B =  b1 b2 C = c1 c2 c3     Find C*A. Transpose C*B.

A:

Q: Let B= (b,,b2} and C = {c1,c2) be bases for R. Find the change-of-coordinates matrix from B to C and…

A: