4- Determine the rank of the following matrices: [1 2 8] [3 4 5] ii- A= 1 2 3 [4 5 6 [3 9 21 iii- A = |1 5 6 l2 7 4] i- A = 4 7 6 9 5 3.

Q: 4- Determine the rank of the following matrices: [1 2 8] i- A = |4 7 3] [3 4 5] ii- A=|1 2 3 [4 5 6]…

A: i. Given: A=128476953  ……1

Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

A:

Q: [2 If A = 3 4 1. 3 2. 6 3. 8 4. 0 x-3 -2 -1 x-27 -1 -5 is a symmetric matrix then x 4

A:

Q: (0) Construct two non-zero 3x3 matrices A and B such that for A its rank is greater than its nullity…

A: two non-zero 3×3 matrices A and B such that for A its rank is greater than its nullityand for B…

Q: Find the rank of the following matrices: 1 2 3 2 3 1 2 4 6 2 4 rank(A)= 1 2 4 2 3 6 3 1 2 4 2 4…

A:

Q: 4- Determine the rank of the following matrices: [1 2 8 i- A =4 76 9 5 3 [3 4 51 ii- A=1 2 3 4 5 6…

A:

Q: 4 2 If A is a non-singular matrix whose inverse is find A. 1 - 2 -1] -1] 1 В. -1 1/2 С. -1/2 1 D. |…

A:

Q: 1. Determine the matrices C 2A + B and D A- 3B if 2 8 -6 -3 3. -3 -2 -4 3 0. A = %3D -6 -1 -8 9. -2…

A:

Q: [1/V14 2/7 2/V14 -4/7 1//21 5/7 [3/V14 2/7 -2//21 [1 4 8 4//21 [14/V14 28/V14 28/V14 20 1 A : 7 = QR…

A:

Q: A and B are 3,3 matrices. Lo lAl =-3 and IBl =2. SO phat is l-2A02|?

A: Properties of determinant:kA=knAAB=ABA-1=1A

Q: Determine the rank of the following matrix. 0 3 5 -4 0 1 0 0 -1

A:

Q: Show that these four matrices form a representation of the Vierergruppe, whose multi- plication…

A: 17.2.2 We have to show that given matrices  I,A,B and C form a Vierergruppe. Concept:…

Q: 4. Verify whether the two given matrices are similar. Justify your an- Swers Question a. 1 A = 1 and…

A:

Q: Find the LU factorization of the following matrices without pivoting 1 2 3 a) A=2 5 4 354 1 -1 1 -1…

A: We have to find the LU factorization of the matrix. L is the lower triangular matrix  U is the upper…

Q: 1 The matrix product 3 is equal to 1 3 O ( ) 3 8. 5 8 3. 5. 8. 3. 3 O (8 5. 3.

A:

Q: Consider again 2 × 2 diagonal matrices: k 0 0 j If k, j ∈ {0, 1, 2, 3, ..., 9}, how many possible…

A: Given 2×2 diagonal matrix k00j k, j ∈0, 1, 2, 3, ..., 9

Q: Compute the indicated matrices, if possible .…

A: Given that, A=1235B=20-13-34

Q: Determine whether the given matrices are linearly independent.

A: Solution: Consider the given matrix: A = 0152-10 Since the matrix has two vectors  v1 = 05-1  and v2…

Q: Compute the indicated matrix by using the following matrices. [ 1 -4 1 -5 0 6 A = 3 C = B = 6. 6 -1…

A:

Q: -1 - 3 7 Let A 1 and A 2 be two matrices in M2. = -6 4 7 Choose the matrix that belongs to span {A…

A:

Q: Find the rank of the following matrix: 3 1 0 0 0 0 rank -2 1 1 4 0 4 2 4

A: A=23100000-21140424 Now, R3→R3+R1 A=2310000004240424 C1→12C1 A=1310000004240424 R4→R4-R3…

Q: 4- Determine the rank of the following matrices: 2 8] [3 4 5 [1 7 6 ii- A=1 2 3 5 3] [3 9 21 iii- A…

A:

Q: Express the matrix as a product of elementary matrices 2 2 07 [1 A = |0 L3 1 1 3 8 7 ]

A:

Q: 1) Classify the following matrices into singular and non-singular matrices 2 4 3 a) 3 b)|-2 -4 -3 -2…

A:

Q: Given the matrices below and that A = LU, complete L-1, U-1, and A-1, 1 -3 -2 1 -3 -2 A -5 16 12 L =…

A: Given The given matrices are A=1-3-2-516121-4-3 L=100-5101-11 U=1-3-2012001 For the inverse matrix,…

Q: Let A and B be two 4 × 4 matrices with rank(A)<4. Then rank(A²B)<4. Select one: O True O False

A:

Q: 3 1 2 Compute the adjoint matrix of A = 3 2 2 1 2 3 Select one: 1 4 а. -7 8 4 -5 3 1 -2 O b. -7 7 4…

A:

Q: 6.- For the matrices [A] g 3 -2 4 -2; [A] =-5 3 3 2 3

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Match the two matrices A, B with their product AB. i Instructions 1 0 2 6 7 4 3 4 5 -3 9 0 6 1 [1 -2…

A: Match the two matrices A, B with their product AB.

Q: Find the ranks of the following matrices. 0 3 0 0 -4 0 rank 1 0 0 0 1 0. rank 0 -2 3 1 rank 8. || 3.…

A:

Q: Let A and B be matrices with size 3 x 3. If only one of these matrices are diagonalizable and if…

A: Given, A and B be matrices with size 3×3det(A-λI3)=(λ-2)(λ2-9)det(B-λI3)=(λ-3)2(λ+2)(a) Eigenvalues…

Q: Determine whether the given matrices are linearly independent.

A: Given: 1234,4321 Let  λ11234+λ24321=0λ1+4λ22λ1+3λ23λ1+2λ24λ1+λ2=0

Q: 3. Diagonalize the following matrix: [2 1 01 1 2 Lo 1] [3 0 A. 0 1 Lo o [1 = [0 2. 1 2 Lo o 1 1 1…

A: the given matrix is A=210120001 the characteristic equation is A-λI=0 where I is the identity matrix…

Q: [3 Given A = 2 2 1 1 3, find [4 1. the lower triangular matrix. 0. 0. 0. 01 a. 2 -1/3 -2/3 -5 01 С.…

A:

Q: Find three 2 × 2 matrices, A, B, and C such that AB = AC with B = C and A = O.

A: Consider the matrices A=0000,  B=1234  and  C=1234. Clearly, B = C and A = O.

Q: Given the matrices below and that A = LU, complete L-1,U-1,and A-1 1 0 0 L = |1 1 1 4 -1 1 4 A = 1…

A: Given that A=14-115-6213-26 and A=LU where L=100110251 and U=14-101-5001

Q: Define the matrices 2, A = 1 ). B- ( ).c-( ). D - ( ) = - (;). 3 4 ‚E 4 3 1 1 2 1 В - C : 2 -4 -2…

A:

Q: ریاضيات هندسية )1( نظري 3 1 Compute the adjoint matrix of A: 3 2 2 1 2 3 Select one: 4 a. -7 0. 4 -5…

A:

Q: 4- Determine the rank of the following matrices: 2 81 [3 9 2 5 6 2 7 4] [1 [3 4 51 i- A = 4 7 6 ii-…

A: See the explanation below

Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

Q: Determine the rank of the following matrices: 0 1 -3 -1 1 2 3 1 0 (ii) 3 1 1 1 (i) 1 4 2 2 6 5 1 1…

A:

Q: 4- Determine the rank of the following matrices: [1 2 8] [3 4 5] [3 9 2] iii- A = 1 5 6 l2 7 4] i- A…

A:

Q: 2. Find the LU factorization of the following matrices without pivoting 1 2 3 a) A = 2 5 4 354 1 -1…

A:

Q: Determine the rank of the following matrix. 0 2 3 -4 0 1 0 0 -1

A: rank of matrix

Q: a. Prove that (A'B*)-1= (A-B-1)* and B are 3 x 3 matrices and %3D b. If |A| = 4 |B|= -1 compute…

A: I have used the property of  transpose and inverse of product of two matrices and then show the…

Q: 4- Determine the rank of the following matrices: [1 2 8] i- A = 4 7 6 9 5 3] [3 4 5] ii- A=|1 2 3 [4…

A:

Q: 2) Find inverse matrix using Gauss - Jordan Method if available 1) [1 3 41 A = |1 -5 L3 -2 41

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

Q: 4- Determine the rank of the fcllov-ing matrices [1 2 8] 7 6 ii- A=|1 2 3 5 3. 13 4 3? i- A = |4…

A: for a 3*3 matrix if determinant is not equal to zero then rank is 3  if it is zero then we calculate…

Q: 2. Orthogonally diagonalize the matrices. -4 4 1 5 (a) 5 1 (b) |-4 4 9

A: The given matrices are; a)  1 5       5 1 b).   7  -4  4        -4  5  0         4  0  9

Q: As = 8 6 4 A," = 1/3 - 1/6 /2 4 2 2 2 4 4 - 1 - ½ 5/6 1/3

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.