2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A: Given that A is real ( All entries are real)  square matrix of order 250×250. The trace of any real…

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: If an m x n matrix U has orthonormal columns, then UTU = I.

A:

Q: 5.)Write the aua mented matrix for the syshem X, +2X,-X, tXc =l =マ+ t bulo

A: We have to solve given problem:

Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

A:

Q: 2) does the following matrix is orthonormal and orthogonal? Why? R = 2

A: Orthogonal and orthonormal matrix

Q: Let A and B be n × n nonsingular matrices. Find nonsin- gular matrices P and Q so that PAQ = B.

A: Given that A and B  are n×n non singular matrices. An n×n matrix A is non singular only if A is…

Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

A: Given matrix is A=2   11   2 and condition is Ax=3x

Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

A:

Q: If A is 3 x 5 matrix with rank 1, then the number of special solutions to Ax = 0 is %3D O is

A: Since the rank of the matrix = 1. So the number of free variables = 5 - 1 = 4.

Q: Let Q be a matrix with orthonormal columns, then QQT = 1. :Select one True False

A:

Q: 2) Suppose that A and B are nxn matrices that satisfy AB=AB. Show that AB = AB.

A:

Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

A:

Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: Express the following matrix as a product of several elemen- tary matrices. 1 3 E 2 3 ||

A:

Q: Suppose that A and B are matrices having n rows. Prove that M(A|B) = (MA|MB) for any m ×n matrix M.

A:

Q: Find a 3 × 1 matrix x with entries not all zero such that

A:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then Oa Q'Q +1 Ob QQ" - I OcQ" - Q Od. Q"Q-…

A: The detailed solution along with the final answer is described below.

Q: 5. Verify that the product of the non-singular matrix and its inverse from the previous problem is…

A: (5) Given matrix A=32−22 and its inverse is A−1=1102−223. We have to verify that AA−1=I2…

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: if A is m xN matrix pivot in every row, then Ax-b has that has a a unique solution for each b in Rm

A: The given question can be solved as shown in step2.

Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

A:

Q: 4. Prove or Disprove: For anynxn matrix A, A A = AA.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: Let A be annxn matrix and B=A+T, where / is the identity matrix, then it is possible for A and B to…

A: Given matrix combination is B = A + I

Q: Solve for the matrix X if AX(D+BX)-! = C. Assume that all matrices are n x n and invertible as…

A: It is given that AXD+BX-1=C. It is required to solve for the matrix X such that all matrices are n×n…

Q: 5. If xy + 2xu + 3xv + uv-| = 0, 2xy + 3yu – 2xv + 2uv + 2 = 0, ſind the Jacobian matrix [ ].

A: Let, F(u,v,x,y)=xy+2xv+3xv+uv-1Gu,v,x,y=2xy+3yu-2xv+2uv+2 By the chain rule,…

Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: Solve for the matrix X if AX(D + BX)-! = C. Assume that all matrices are n X n and invertible as…

A:

Q: Suppose that A, B, C and D are n × n matrices satisfying the equation ABC = D. Show that if DA is…

A: Given:Suppose that A,B,C and D are n×n matrices ABC=DInvertible matrix:A square matix is invertible…

Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

A:

Q: Suppose U is mxn matrix. Explain why if U has orthonormal columns, then we must have m greater than…

A: Let U be a m×n matrix.We need to show that if U has orthonormal columns, then we must have m greater…

Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

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: If the rows of an mxn matrix A are linearly independent and Ax=b is consistent then it has unique…

A:

Q: Suppose that Q is a matrix with the property Q−1 =QT . Show thatqij = Qij/det(Q)

A: Given: Q-1 = QT To Prove: qij = Qij/det(Q) Formula Used: If A is a square matrix, then its inverse…

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

A:

Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

A:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then O a. QQT = I O b. QQ" + I Oc Q" = Q1 O…

A: Given Q is a 3×2 matrix then QT is a 2×3 matrix.

Q: There are sixteen 2 by 2 matrices whose entries are 1 's and O's. How many of them are invertible?

A: A matrix will be invertible if the determinant is not equal to 0.

Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo+ kJ where Mo…

A: M is a 3 x 3 magic square matrix with weight w. We take weight, w=15 The matrix of M is  Add any…

Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

A:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then O a. QQT = I O b. QQT + I OCQT = Q1 Od.…

A:

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…