and Consider the subspaces of V = R¹X3. Find a matrix X EV such that UnW = span{X}. X=[ U = span{[-1 -1 -2],[-4 −1 −9]} Wspan{[4 -2 2],[-2 1 -13]}

Q: Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 +…

A: Here we will find matrix of linear transformation

Q: Find a base for the line space of the matrix and determine the line rank.

A:

Q: Is the span of a matrix A is the same as the column space of A? T or F

A: We shall answer this question in next step

Q: 2. Express each of the following quadratic forms as a matrix product involving a symmetric…

A:

Q: Let A be an invertible 3 by 3 matrix. Assume that PA²P-15ATA². = Then det(A) =

A: Step 1:   Step 2: Step 3: Step 4:

Q: Find a basis of the following linear system. { X1 2x1 x1 3x3 4x2 x2 + x3 + 2x2 + + 3x3 + 7x4 7x4…

A:

Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

A: Given: 2x1+4x2-x3=157x1-3x2+3x3=-44x1-3x2-8x3=19 We have to find the inverse of the coefficient…

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

A:

Q: Let V = [- 7, – 7,0] and V½ = [0, 3, – 4]. Use the Gram- | Schmidt procedure to construct an ordered…

A:

Q: Determine whether b is in col( A) and whether w is in row(A)

A:

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Find the following matrix-vector product: [13 20 0 -1 3 -2

A: The given matrices

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

Q: Do NOT row reduce! (a) Write the augmented matrix whose row reduction would find [x]B . (b) Write…

A:

Q: Let A be a 2 x 2 matrix, and suppose rank(A) = 1. Prove that the rows of A are scalar multiples of…

A: To prove that the rows of matrix A are scalar multiples of each other given that rank(A) = 1, let's…

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / infinity, where…

A:

Q: Show that if two real symmetric matrices A, B are congruent then there is a linear change of…

A: The objective of this question is to prove that if two real symmetric matrices A and B are…