1 -6 7 Let A = 0 2 X 3 and b L2 -12 14] If possible, write b as a linear combination of the columns of A. b= -3 -1 OWe can write b as a linear combination of the columns of A. -6 7 2 3 -12] L14] Ob is not a linear combination of the columns of A. +-1 +6

Q: If matrix A is 2 x 5 and the product AB is 2 x 4, then what is the order (or size) of B?

A: is a  matrix is  matrix.We have to find the order of

Q: Determine if the columns of the matrix A = - 2 1 4 0 84 4 t 0 are linearly independent.

A: Here we need to show that columns of matrix A are linearly dependent or independent.We all know that…

Q: use some form of technology to show that the given matrix is nondefective

A: Given : A=ababababa To Show : A is non-defective.

Q: Find the LU factorization of A = A = 9- -4 E -4 That is, write A = LU where L is a lower triangular…

A:

Q: Question # 2: For the following matrices, give the geometric description of space spanned by their…

A: The columns spans a plane. For full details see below.

Q: Let A be a 4×5 matrix with 4 pivots. Do the columns of A span R4? Do they span R5? Justify your…

A: As A is a 4 x 5 matrix with 4 pivots so, it has a pivot in its every row. So, yes the columns of A…

Q: Let A be a 3 x 3 matrix, and B be a nonsingular 3 x 3 matrix, such that det(A) = 12 and det(B¹A)=…

A:

Q: [3] 37 Let A = Write 2A. Is det(2A) equal to 2det(A)?

A:

Q: List the pivot columns of matrix A = 1 -4 0 3 1 -9 2 -3 -6

A:

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: Using divided difference formula, we calculated a, to be 1. If x; - x;-1 = 1, and f (x,) = f (x2),…

A:

Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

A:

Q: Find an LU-factorization of the matrix : 4 1 2 5 1 2. 3 - 7 6 14 16 11 1

A: Recall: LU factorization by using Gaussian Elimination method

Q: Q10.5 If A is a 2x8 matrix and if B is mxn , figure out the value of m if BTAT is a 20x2 matrix.

A:

Q: Determine whether or not ( ABC )T = C"B"AT for matrices: A, B, C

A: Given- ABCT=CTBTAT To Determine- Whether the above statement is correct or not for matrices A,B,C.…

Q: If a matrix A is such that, 3A³ + 2A² + 5A + I = 0 then its inverse is?

A:

Q: Is the following matrix diagonalizable¹? 3 B=0 0 -3 1] 3 1 0 3

A:

Q: Show that for a square matrix A, AAT is a symmetric matrix.

A:

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: B) find the transpose of the matrix A C = 3 2

A:

Q: Determine the rank of matrix A, where: A = 1 0 -1 39 0 0

A:

Q: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

A: .