15. Suppose a 3 × 5 matrix A has three pivot columns. Is Col A = R³ ? Is Nul A = R² ? Explain your answers.

Q: 4 1 34. The rank of the matrix A = 2 -1 is -7 -14 4 8 -1 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4

A: To find The rank of a given matrix A.

Q: If the inverse of matrix A = 2-1 2. k 7- A 2c kc b+1 -k Findl the value of ktb+c =?

A: The solution is given below in the next step:

Q: 1 4 is multiplied by is If matrix is equal to zero, then matrix A 8 B. 1 C-4 D. o

A: We have to find the matrix

Q: Find (3)BA+ (4)AC, if possible. A = [00-2] 0-2 0 B = [] C - 3 0 1 12 1 1 -2 -1

A: The given matrices,.The objective is to find .

Q: transpose.

A:

Q: For the matrix A = evaluate each side of the following equation and state whether the equation is…

A:

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: Suppose AB = I, . Show that the equation Bx=0 has only trivial solution. Explain why the matrix not…

A: Suppose that AB=In (then x n  identity matrix). The objective is to show that, the equation Bx=0…

Q: II. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = -3 2 3 9 3 2 6 8 ㅋ

A:

Q: 12. Find A + B, where -1 3 5 2, B = 0 -2 -3 0 5 2 -3 2 -3 a) A =-1 9 -3 b) A = B = -4 -3 5 -2 -1

A: a) Given A = 104-1220-2-3B = -13522-32-30 Then A+B = 104-1220-2-3+-13522-32-30=…

Q: Find an LU-factorization of the matrix. (Your L matrix must be unit diagonal.) [33] 56 0 LU = 188=

A: The given matrix is A=-71560. The LU-decomposition of a matrix A is factorization of matrix such…

Q: Determine the matrix if it is a linear combination of O A.c = 5; d = 8 O B. c = -5;d =8 O C.c = 8; d…

A: 12cd = a1-1-1-1 +b3159 + m41611 + n-1234 Therefore, we get a+3b+4m-n = 1…

Q: Diagonalize the following matrix. - 49 - 30 - 75 46 P = D = 00

A: As per our guideline we are supposed to answer only first question of a multiple type questions.…

Q: 2. Estimate Y = +&X+ e using matrix method. 15 15 20 30 32 35 40 Y 14 13 16 25 27 34 44

A: Given the data as X 15 15 20 30 32 35 40 Y 14 13 16 25 27 34 44

Q: 5. Diagonalize the following matrix. 3 B = -3 4 9

A: Let A = aijn×n be any n-rowed square matrix and λ is a scalar. The equation AX = λX is called the…

Q: 9. When can a square matrix be diagonalized? When can a square matrix be diagonalized orthogonally?

A:

Q: Below is a question as an example. You author, in the sample question of the C matrix, write your…

A: Matrix row operation problem....

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: Do the columns of A span R*? Does the equation Ax=b have a solution for each b in R*? A = 3 0 1 -3…

A: Given that the equation :

Q: Suppose that A, B, C, D, and E are matrices with the following sizes: A(4x 5); B(4X 5); C(5 X 2):…

A: Size of matrix

Q: 3. Let A be a 4 × 4 matrix. Suppose the matrix equation A has solution set 2 -t+8 what is the…

A: Put t=1, s=1. Now we have  A12-1+111=A1211=20-23 Consider the set 12-t+sts-1211

Q: 6. Use row operations to reduce the mats product of pivots.

A:

Q: Suppose A is a 4 x 8 matrix with 5 pivots. What can be said about the dimension of the column space…

A:

Q: How many pivot columns are in the following matrix? The number of pivot columns is R = 1 0 0 0 0 0…

A: Given Data: Let us consider the given data, R=103-200000100000 To Find: The number of pivot columns.

Q: a2 If the columns of the matrix A = -1 are orthogonal, then 2 -1 2 az = 1 a. O b. az = -1 C. a3 2 d.…

A: If column of matrix  A are orthogonal then  B = A^T A  Elements B(i,j) = 0 for i is not equal to j.

Q: Given the matrices A and B, solve for X. 18) 3X - B= A. 5 -2 3 and B= -1 -1 A = -4

A: 3X-B=A

Q: Express the column matrix b as a linear combination of the columns of A. (Use A₁, A2, and A3…

A: The given matrix and a vector, and .The objective is to write the vector  as a linear combination of…

Q: A 17 B 10 Ⓒ 7 D 13 [24 Consider the matrix = 1 6 2 8 51 4. What is the sum of a13 + a32 ? 9

A: Given that the matrix  A=245164289   .

Q: Suppose that 4x7 matrix has 4 lead terms. Then collA) = IRt and NIA) = R³ True O False

A: