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 = |1 5 6 l2 7 4 i- A = 4 [4 5 6

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: (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: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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: 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: 2 2 3. Transform the given matrix to RREF -2 1 1 -1

A: The given matrix is; 3 2 2 -2 0 1 1 -1 0. Repost the next question.

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: Refer to the following matrices. -1 5 2 3 A = 2 -5 5 1 %3D 2 2 Compute 2A - 3B.

A: See the attachment

Q: Which of the following matrices are in RREF? (: ) (1 10 7 0 1 9 0 0 1 1 14 1 1 - 1 0 0 5 1 1 10

A: Solution

Q: Find the rank of the following matrix. 3 6 5 12 1 2 2 1 2 1 5 2

A: To find the rank of the given 3x4 matrix?

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A" A-1)?

A: Given that A,B and C are 3*3 matrices. To find det(A^TA^-1)

Q: Compute the indicated matrices, if possible .…

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

Q: 8. What is the rank of the following matrix: -2 0 1 -4 1 2? 3 -6 1 3, 2

A:

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: Given the following matrices: X 2 -3 5 1 -2 -4 5 6 0 5 7 4 Show that (XYZ) = ZTYTXT Y = -3 6 2 6 -4…

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: 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: 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: 1. Determine the matrices C = 2A +B and ) = A-3B if 8 -6 -3 1 -2 3 2 -3 -4 A = -6 %3D -1 6. 4 -7. 2…

A: C=2A+B=28-6-31-20-65-1-280+32-3-4302-86-14-7=16-6-31-20-65-1-280+32-3-4302-86-14-7∴C=19-10-9-2-10-10…

Q: Given A = 1 1 0 3 Compute 5A *Matrix

A:

Q: 4. 1 0 13 4 1 -2 15 -1

A: 100010001·2457134-215-17=1·2+0·7+0·-21·4+0·13+0·151·5+0·4+0·-170·2+1·7+0·-20·4+1·13+0·150·5+1·4+0·-1…

Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: 1 2 Compute the adjoint matrix of A 3 2 2 2 3 Select one: a. -7 4 -5 7 -7 -5 3 -1 -2 %3D -7 -5 41 d.…

A: We have given a matrix and we have to find the adjoint of A.

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: Consider the following matrix: 3 4 A 1 2 -1 b -3 1 If rank(A) = 2, a + b =?

A:

Q: 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…

A:

Q: Given the matrices below and that A = LU, complete L¬1,U-1, and A-1. 1 -2 -1 1 01 -2 -1° A= 2 -3 -5…

A: We use Gauss elimination method to find L-1, and U-1. After that by using (LU)-1=U-1L-1, we find…

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: 4. Find the LU factorization of the following matrix (1 1 1V A = 2 3 2 3 8 2

A: according to our company guidelines we can answer first question (if specific is not asked) or only…

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: Compute the LU factorization of each of the following matrices.

A:

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: 1. Find the rank of the following matrices -2 [ 1 2 3 1 2 -2 -3 -1 3 2 (i) ( ii) -2

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: Given the matrices: 2 0 4 7 4 1 E = 0 1 8 7 9 5. 0 0 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: 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: 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: Evaluate: 1 3 -2 24 45 3 1 1 10 1 05 5 -3 13 6 -2 2 9 4 5 13 2 369 5 -3 B 13 6 2 9 The matrices are…

A:

Q: 3. Consider the following matrices: -4 3 -7 4 7 -4 A = В — 2 8 -3 -2 3 -2 -5 -1 -5 3 -7 D = and E 2…

A: The given matrices are                               A=3  -7    42     8 -3…

Q: 6 6 4. -6 10 -1 23 10 0 -2 -11 3 B = -5 -11 9 -3 1. Given the matrices A = C =[-3 2 9 -5 7]. 1 -1 3…

A:

Q: Determine the rank of the following matrix: -2 3 -1 1 4 3 5 11 -6 5 -3 7 -10 4. 0 8 -8 -1 2 02

A: Try to form row echelon form of the given matrix  We know,   rank of matrix = number of non zero…

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

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.