Let A=[aij ] be an m xn matrix and k be a scalar then kA is equal to : * [kaij]mxn [aij/k]mxn [k2aij]mxn

Q: Construct a matrix whose column space contains (1, 1, 1) and whose nullspace is the line of…

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: Show that A= 4 * eye (4) - ones (4, 4) is not invertible: Multiply A* ones (4, 1).

A: We have to show that:  A= 4 * eye (4) - ones (4, 4) is not invertible

Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: Let Q be the n × n real matrix in which each entry is 1. Show that det(Q−nIn ) = 0.

A: Given:         Q=11....111....1....................11....1n×n,…

Q: If A is an orthogonal matrix and c is a scalar, then cA is orthogonal. True or False?

A: We have given a statement about orthogonal matrix and we have to state if it is true or false. For…

Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: Let A = [kaij]nxn, B = [aij]nxn, be an nxn matrices and k be a scalar then det(A) is equal to: *…

A:

Q: Let A  be a 7x5 matrix (7 rows, 5 columns). You know that the column space of A  has dimension 3.…

A:

Q: Construct a 3 x 3 nonzero matrix A such that the vector is a solution of Ax = 0.

A: Given conditionAx = 0          .................(1)x = 111 is a solution to Ax=0,Let matrix A be - A…

Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

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: Write down the 3 x 3 matrix that rotates a 2D point by angle about a point 0 p = (xp, yp).

A: Consider point .To write the  matrix that rotates a  point by angle  about a point .

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

A: