1 3 -3 5 Let A = 2 6| and B -6 10 | be given. If exists, what is the sum of the elements of the 3 6 matrix X = [X], where AX = B ? 12 6 (a) There is no X. (b) 0 (c) –11 (d) 10 (e) 21

Q: 1 0 0 A is a 4 x 3 matrix. If BA = 0 1 0 then the size of B is 0 0 1 O 3 x 4 O 4 x 3 O 3 x 3 0 4х4

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Q: 5. Let 2 0 A= H 2 2 0 -3 0 - find the matrix noms

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Q: 4. If G is a 3 x 1 matrix while H is a 1 x 3 matrix then A. GH is 3 x 3, HG is 1 x 1. B. GH is 1 x…

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Q: 1 -14 -9 Find the rank of the matrix 03 01 O2 04 4. 3. 4.

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Q: 4. If G is a 3 x 1 matrix while H is a 1 x 3 matrix then A. GH is 3 x 3, HG is 1 x 1. B. GH is 1 x…

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Q: 1 0 3 -1] 6. Partition matrix A= -3 5 1 into four 2 x 2 blocks. 1 | 1 -3 7 1

A: As per our guidelines we only solve one question and rest of the question will be reposted.

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

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Q: 3 1 A is a 3 x 4 matrix. If AB = -4 then which of the 5 -2 7 following is the size of B? О Зx2 O 2 x…

A: Since, A has size, 3×4 and, the product AB has to be defined, so, we must have, the size of B tombe…

Q: 2. Let 2 25 IO -1 23 7 013 and B= 32-1 23-2 A = a) If possible, invert the matnx A b) then solve the…

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Q: 4. Suppose we have n x n invertible matrices A and B. a. Is the following property true or false?…

A: 4 Given Aand B are the n×n matrices. a We have to check whether the property AB2=A2B2 is true or…

Q: 3 5. Suppose that A is an invertible matrix with A-1 = a. Find A. b. Find the 2 x 2 matrix X so that…

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Q: 17 -2 14 0 The null space for the matrix 30 1 -2 3 6 1 -1 0 4

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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: [2х 81 2) For what values of (x) does the matrix : 1 a)singular b) non-singular

A: Given matrix is  A=2x81x Now,  A=2x81x=2x2-8=2x2-4 So, A is singular when A=0 which occurs when x2-4…

Q: 8. 3 a) Let A = ( 6 1 3 ,B = 6 -2/ %3D 1 Then find the matrix AB. -4 -1

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Q: -9 -9 -42 -36 Let A = and let B = 3. -8 33 15 Solve the matrix equation for X : 3X = 3A –B. ЗА -В.…

A: Divide both sides by 3

Q: 3. The matrix Q [(-²/2 -2²) (²₁2 --8383 1) G1₁ -1 a (a) positive definite. (b) negative definite.…

A: Given :Q=2-23-1-22113111-1115

Q: 2 3. 1] Given that matrix P =0 2. Find the matrix A such that A = PBP 1, where 1] -1 1 -2 0 01 B is…

A: Given:The matrix P=2310-12101 , B=-200030006To find:we have to find the matrix A such…

Q: \8 9 (3 2 1 5. Find the co-factor A21 of the matrix 0 -1 \2 2 2 6. Find the co-factor matrix of -1…

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Q: 2 3 3 Let A and B 3 5 given that AX+X=B. Find the (1,2)-entry of matrix X -3

A: Matrix multiplication, for matrix A and B can only be done if the number of columns of A is equal to…

Q: above one If A, B and C are invertible matrices, then (3A CB™)-1 is A-5 B-(C-1)" equal to the above…

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Q: 5 3 3. Given the matrix C = find a matrix X such that 2 2 (а) СХ + С — I (b) XС + X —I (с) (XT —…

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Q: -10 1 Let A = Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = I,. Is it…

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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: 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: 5 3 3. Given the matrix C = find a matrix X such that 2 2 (b) XС + X —I (c) (X" – 21)-1 =C

A: To solve the following matrices

Q: 0 - 3 Compute each matrix sum or product if it is defined. If an expression is undefined, explain…

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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: 8. (i) For what type of square matrices A will the algebraic system Ax = 2x have solutions other…

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Q: 1 1 2 1 1 and B = 1 1 2 1 Let A = -1 -4 1 -2 -2 5 -4 1 -6 5 -4 1 2 4 -2 To show A ~ B, it is…

A: Given that A=11211210-1-41-21-25-4B=102012101-65-4204-2 To prove : A~B If two matrix A and B are…

Q: 6: [1 The rank of the matrix A = 4 15 True O False 2 2 5 7 31 6 is equal to 3. 9

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

A: We have given the matrices A, B, C such that CD-AB=0 We have to find the matrix D

Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: 4 3. If A = x+2 is an invertible matrix , then x can't take value 2х -3 х+1 (a) -1 (b) 2 (c) 3 (d)…

A: 3. Given A=4x+22x-3x+1 is an invertible matrix.  If A is invertible then detA≠0 Let us find detA…

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: -3 -7 -2 Show that A = -3 3 and B = -3 0. are similar matrices by finding an invertible matrix P…

A: Given: A=-3000-3300-4 and B=-7-6-20-30690 To show: A and B are similar matrices by finding an…

Q: 0 1] 1 by Gauss-Jordan elimination, let the augmented matrix 1 -1 2 While you are inverting the…

A: Let the given matrix be  A=1011111-12 To invert the matrix by Gauss -Jordan elimination method,…

Q: 1 2 4 Suppose matrix A: A=3 16 x 3 2 Determine the value of x if matrix A is singular.

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Q: 1 4 5 Let A = 8 8a -6 . If a = -1 then the rank of a matrix a |1+a? 8a+4 2a+21 A is

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Q: [4 1 21 tA-3 4 2. B-1 -2 3, and C-5 0 2 Lo 3 2] [-1 0 5 [1 2 -3] [1 4 -3) 1 -1 1 [s 20 Find the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (9) If 2 0 0 1 3 A-'B-1 and A = 2 -1 evaluate the matrix B.

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Q: 1 1 1' A is a 3 x 5 matrix. If CA = | 1 2 1 then the size of C is 1 1 2, O 3x 5 O 3x 3 O Undefined O…

A: Given: A is 3x5 matrix CA=111121112

Q: 1 3 -4 -3 Find the nullspace of the matrix A = 0 1 0 0 -3 1

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Q: - 1 1 0 -1 Let b = 2 and suppose that A is a 3 × 3 matrix whose inverse has the form A- = 2 where c…

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Q: 1 1 1' Let A be a 3x3 diagonalizable matrix, P 1 1 p-1- 0 1 2. 0 0 -2 D 0. If P-'AP = D then A2 is…

A: I have explained all necessary information in the solution part

Q: 2 3. Let A be an invertible matrix such that A¯¹ = 0 l-1 2131 010 Solve the system (2A2)x= b, where…

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Q: 1 0 0 -1 -2 Ais a 3 x 5 matrix. If AC = 0 1 0 3 4 then the 1 -5 6 size of C is

A: Given : A is a 3 x  5 matrix From the given matrix AC AC is a 3 x 5 matrix We know that , to…

Q: 9. If M = 2e -Ze-is Is a fundamental matrix for X' = AX, then the exponential matrix et is 2e-…

A: Column of the Fundamental matrix are the solution of the homogeneous differential equation.