1 -2 0 4 3 Calculate the rank of the matrix P = 1 1 -1 -5 -1 3 8 2 -12

Q: 1 4 2 3) Find the null space of the matrix A = |0 L-2 1 1 -1 -8 -4 -2

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Q: [1 2 31 What is the trace of matrix A? A = 4 -2 3 [4 7] O -6

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Q: 2 1 -1 3 1 2 1 2 0 b) Calculate the rank of the matrix P = 3 1 1 1 |-1 -5 -3 -7 3

A: Given,

Q: (1 3 2 3 2 4 Question 3. Consider the matrix A = . Is there an orthogonal matrix P and a diagonal…

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Q: -1 10 2 4 5 2 10 coeFFICient of matrix (A) 2 3 -5 2

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Q: 1 0 -2 Given the matrix A = 4 -3 -4 |, find -2 -2 1 det(A).

A: We will solve the determinant by the first row.

Q: -2 1 -1 -3 1 3 b) Find the Rank and Nullity of a matrix A = -2 -1 1 -1 3 3 9 0 -12

A: Concept:

Q: 2 -1 B= 4 5 2 2 5 Let A= 3 7 4 3 8 Find the matrix D such that CD-AB=0.

A: We have to find matrix D

Q: 5 -3 Find the matrix A if (I+ 2AT) ¯ = | 1: -2

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Q: 1 0 2 2. Given the matrix, A = 2 -1 3 find A-1, using the Gauss-Jordan method 8

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Q: -5 -8 0 12. Show that the matrix A = 3 5 0 is involutory. 2 -1

A: We can easily check  whether a matrix is involutory or not. For this, check the square of a matrix…

Q: 1 2 3 -27 2 -5 1 If A then the = 3 -8 -12 -1 rank of the matrix A is

A:

Q: 2 1 -1 3 1 9. Calculate the rank of the matrix P = | 2 1 2 0 3 1 1 1 |-1 -5 -3 -7 3|

A: P=210-131212003111-1-5-3-73

Q: -2 5 Find the characteristic equation of the matrix 3 5 C. 22 – 32 – 25 = 0|| D. 2? +72 - 25 = 0 A.…

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Q: 2 1 0 -1 3 1 Calculate the rank of the matrix P = 1 2 0 3 1 1 1 -1 - 5 -7 3 -

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Q: ' 1 2 3 What is the rank of the matrix A = -1 1 3 0 -1. O 2 O 3 O 1

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Q: 2 1 4 6 Find a matrix X that satisfies A(X+I,)=B, where A = and B = 6 5 3 5

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Q: 24 --8 Find the rank of the matrix A =0 1 -2 4 8 -18 rank(A) =

A: given matrix is  A=-24-801-2-48-18 to find the rank of matrix

Q: 4 8 -12 A--16 -32 49 20 40 -55 Express A in the form A LDU, where L, is lower triangular with 1's…

A: Lower triangular matrix: A square matrix in which all the elements above principal diagonal are zero…

Q: (2 3 0 Question 1. Is the following matrix positive definite? A = 3 4 0 ]? 0 0 3 Yes No

A: Solution..

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

A: Rank of the matrix

Q: 1 -2 0 4 3 1 1 Calculate the rank of the matrix P = -1 -5 -1 2 -12 3.

A:

Q: 1 -2 0 4 3 18. Calculate the rank of the matrix P 1 1 -1 -5 -1 8 2 -12 3.

A: Rank of a matrix is the maximum number of linearly independent rows of a matrix. The rank of a…

Q: (-1 7 -5 7. Let A = -4 11 -6). Diagonalize A if possible or explain why the matrix A is not -4 8 -3.…

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Q: 2 5 31 5. Write X = |-3 6 0 as the sum of a skew symmetric and a symmetric 4 1 matrix.

A: Given X=253-360411 Let us find the transpose of the matrix, XT=2-34561301 X+XT=253-360411+2-34561301…

Q: 3] [1 2 Find A¹ of The Matrix A = 3 2 -1 3 1 2]

A: As per the instruction, we will be answering the first one. Given: Now,…

Q: 3 5 -3 and D = 3 Calculate the matrix CD where C = 1 1 4 1

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Q: 1 3 1 -1 0 1 Consider the matrix A = -3 2 1 -2 1 4 1 6 1 3

A: Let us apply elementary row operations on the augmented Matrix [A|b] to reduce it in row reduced…

Q: 1 0.1 0.9 3 -12 6 Given Matrix A = 4. 1 -5 5 1. 17 6 -2

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Q: 3 -1 8 1 |-6 4 -3 D = 10 4. Decompose matrix D.

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Q: (3 5 0 For the matrix A =(2 5 4 \2 7 9. what is the element in the first row and third column of the…

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Q: -1 4 What is the minor of the element 6 in the matrix -8 0. 1 3. O-7 O 14 07 -14

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Q: 2 0 0 3 -2 0 1 -1 Consider matrix A = -7 2 4 -2 0 0 5 Calculate det (A³) 1.

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Q: 2 -4 1 Decide by inspection whether the given matrix is invertible -4 -3 1

A: In this question, we have given a 4 x 4 matrix with real entries. A=20001-4005-4202-312 To check the…

Q: 0 2 1 2 4. Find the rank of the matrix N = 2 10 1 201 4

A: We have been given the matrix  Note - Since you have posted with multiple questions so, we will do…

Q: (1 -2 9 For the matrix B = ( 0 \1 Y 3), if |B| = 0, what is the value of y? 3, 1 А. — 3 В. — 4

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Q: 1 3 Find a QR factorization of the matrix A = 1 4 0 2

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Q: 2. -1 4 21 -4 4) Find the LU factorization of the given matrix A= 3

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Q: Q-4 (a) Determine the range, kernel, rank and nullity of the given matrix, [2 1 2 3 1 -3 -1 2 1 4 3…

A: given A=2312003-1211-324323030 to find- range , kernel , rank and nullity of the given matrix

Q: 16. Transpose the Matrix-2 a. C. 312 d. b. 1 -1 12 2 30 TINTO 1 2 -2 -1 3 1 −1 2 -2 2 • -2 0 2 −1] 2…

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Q: 4] -9 0 -8 1 1 -2 -2 13 Consider the matrix -4 3 -1 2 1

A: let B=1-2-21342-43-90-121-81 claim- to find the right inverse of the matrix

Q: 8 -6 Find the matrix P that diagonalizes A and the resulting diagonal matrix D. -2 4 4 3 1 D= P =…

A: The solution is given as follows :

Q: 2 -2 1 Given the matrix P = ( 5 3 find det(P). -1 1

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Q: (1 3 4 Q3: LET A = ( 3 0 4 1 2 -1 1- find |A|. 2- Determine if A symmetric matrix or not ? why ?

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Q: 0 -2 3 0 B = -2 4 ve C=1 -1 2 0 FIND MATRIX a) 2-3A" b) AB c) C" B

A: The given matrices are A=1314, B=30-1-240  and  C=0-21-120 . (a) Evaluate I2-3AT as follows.…

Q: -2 0 4 3 1 -1 -5 -1 1 b) Calculate the rank of the matrix P = 8 2 -12 3.

A: P=1-2043110-1-5-18382-12

Q: 3 0 1] 0 2 1 5 2- Find A. A-1 if the matrix A is given by: A =| 0

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

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