Q-3: [1 0 a) Let A = 2 Lo 2 2 a . Find all values of a for which the matrix A has inverse. -al Find A1 (in terms of a) for the cases where it exists. [2 2 3 6 b) Let A = 1 4 8 By transforming A to upper triangular form 4 -1 Lo 1 -3 -41 find |A|.

Q: 4. 1 a) Find by Gauss elimination, the inverse of the matrix, 2 -1 -2 2. 421

A: Since you have asked multiple questions, as per our company guidelines, we will solve the first…

Q: 2 01 [1 i) Find the inverse of the matrix A = |1 3 3, using elementary row operations. Lo 1 2.

A:

Q: 1 2 Let B:= | 0 0 4 -1 0 2 7 a) Reduce B to the identity matrix using elementary row operations. b)…

A:

Q: 1 2 2 Given that matrix A = 2 1 2 2 2 1 i. Show that A? – 4A – 51 = 0 where I is an identity matrix.…

A:

Q: 1 -2 3 Evaluate A² – 3A+9i where A=|2 3 -1 and i is unit matrix -3 1 2

A:

Q: Given the matrix R = ( 2 −1 1 3 ), i. show that R is non-singular.  ii. find R-1 , the inverse of…

A:

Q: [-5 Given the matrix A = -1 and the matrix B= 4 | 2 , use diagonalization to show that A and B are…

A:

Q: (a) Write down two 2 x 2 non-zero matrices A and B such that AB = 0, the 2 × 2 zero matrix. 3 4]…

A:

Q: 2 Q3: If A = X ly - 1 z + 10 the matrix does not have the inverse. Then, write the matrix A. 32 -31…

A:

Q: -2 3 4 1 -1 and B = -2 -7 Let A = 9. 9. -3 3 -5 -9 -8 8 Let C = AB. What value is C12? If C does not…

A:

Q: -1 1 (ii) Find the inverse of the matrix A, where A= 2 1 -3 1. 1 Hence solve the equations x- y + z…

A:

Q: 5.1) Find the matrix A if det(A) =2 and the classical adjoint is -1 - 2 ad j(A) = - 6 1 6. 24 4.

A:

Q: 1 1 1 11. Let A =| 1 2 3 and D = 3 Com- 4 5 5 pute AD and DA. Explain how the columns or rows of A…

A:

Q: [1 2 1 Given that matrix A= |1 -1 0, find the matrix A². If A³ – A² – 6A = I %3D |3 1 1 where I is…

A:

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: 4 Given matrix A = 1, find x such that the matrix is singular. a. 0 с. 3 b. 2 d. 6

A: A matrix is said to be singular, if it's determinant is zero.

Q: 1 2 3 5. (a) Find the inverse of the matrix A = 2 4 5 As always, show your work. 3 5 6 (b) Suppose…

A:

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Let A be a 3 x 3 matrix so that: (i) Ax = 0 has exactly two basic solutions. %3D (ii) A – 31 has…

A:

Q: 5. Consider the matrix -1 3 0 0 1 0 3 A = 1 (a) Find A-1, the inverse matrix of A by using your…

A: (a)       So substituting in equation (1), we get A-1=130310-631-51Therefore    A-1=0100-2113-5313

Q: a) Let A = 2 0 lo 2 -al а Find all values of a for which the matrix A has inverse. Find A-1 (in…

A:

Q: 1 2 3] 1 1 2 find AB 2 1. c) If A = 2 -2 and B %3D -1 1. d) Using matrix inversion to solve the set…

A: In this question first we have to check that one matrix is inverse of another one and after that we…

Q: 5 a 1 28 6 2 Find all a and 3 > 0 so that the matrix B = is 2 a diagonally dominant;

A: Consider a square matrix . Then the matrix is said to be diagonally dominant if it satisfies the…

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

A:

Q: Q2 / [A] is a matrix and [B] is a matrix , if you know [B] is inverse of [A], determination of [B]…

A: Here [B] is inverse of [A] which means [A] is inverse of [B].  Also we know that, for any square…

Q: 4 4 -2 þ. if A= |-1 1 3 6 -1/ show that A? = A + KI for some constant k, where I is the unit matrix…

A:

Q: -2 Find the inverse A of the the matrix A = 1 2 1 -2 0 Select one: 5 0 O a. -16 -7 5. Ob. -16 -7 1…

A:

Q: Q-1: a – 2b + 2c 2а + b + c] [2 a) Find a, b, c ER such that A = 3 3 a + c is a -2 7 symmetric…

A: 1. Matrix A is said to be symmetric when AT=A 2. In is the nth order Identity matrix

Q: (iv) Given the matrices 3. 1 1/3 -1/6 A = and B =| 0 1/2 Yerify that AB = BA = I where I is the…

A: From the given problem:   A=3102 ;B=13-16012   As we know that the identity matrix is represented…

Q: Using the matrices, [1 0 1] R1 = 0 1 1 li 0 1l [1 1 1 R2= 1 0 1 li 1 11 Find the matrix that…

A: Introduction: The union and intersection can also be performed between two matrices. Also, the…

Q: (1 2 2 1 2 2 b) Let A =| 0 -2 0and B =| 0 1 Find the elementary matrices E,, E,,E, to multiply A, to…

A: We have to find Row Elementary operations to get Matrix A from Matrix B.

Q: -1 For matrices A and 3 -20 -8 B = 8 show that A +B = 1 , 4 where / is the 2× 2 identity matrix

A:

Q: + [12 1 Let A-3-1 2 [101] Find the cofactor matrix C and the inverse matrix A¹. Show the details of…

A:

Q: Matrices A and B are given as 4-1 (1 2 3 7 A=-1 0 4 and B=-1 -1 2 - 0 2 2) 1 1 -1 1 (a) Find the…

A: The order of a matrix is defined as m×n, where m is the number of rows and n is the number of…

Q: Let 1 2 3 A = 0 1 2 0 0 2 (i) Compute the inverse of A using elementary row operations. (ii) What is…

A:

Q: -1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B²…

A: If A and B are nxn invertiable matrices then(AB)-1=B-1A-1

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

A:

Q: 3 -1 Let A be a 3 x 2 matrix. Suppose we know that u = and v = 2 2 satisfy the equations Au = a and…

A:

Q: -2 1 -1 1 -1 1 3 (a) does the inverse of the matrix exist? Your answer is (input Yes or No): Are the…

A: The inverse of a matrix is said to exist if and only if the determinant of the matrix is non zero. A…

Q: -1 -3 4 -3 4 For the matrices A =| -2 5 6. and B = -2 5 -4 show that | BA|H 4|| B | . -3 4 -2 -1

A:

Q: ind the inverse of the matrix, ... -7 -6 4. Choices: -3/2 1/2 –7/2 3/2 1/21 4 1 3 1 c. 10 [7/2 3/2…

A:

Q: [i -1 2 Find the matrix A if (5A)" =|0 2 0 2 0 |3 -1 4 %3D

A: If A is an invertible matrix then,

Q: 7. ). Find all a and 3 > 0 so that the matrix B : 23 6 2 is %3D В 2 diagonally dominant; 12G

A: For a matrix is to be diagonally dominant, there are three conditions or properties, first one is…

Q: 9. Consider the matrix -- 1 A 2 2 -1 0 а. Write the equation det A = 0 in terms of x, y, and z. b.…

A:

Q: -2 [:] satisfy the equations Au = a and Av = b. Find a solution x to Ax = 2a + 5b. 18 Let A be a 3 x…

A:

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…

A:

Q: [1 1 1] 4. Let A =|1 2 3 and D =|0 li 4 5] [2 _0 0] 3 0 Lo o 5] a) Compute AD and DA. « b) Explain…

A: The given question is related with matrix multiplication. Given that,                  A = 111123145…

Q: Express matrix A and its inverse as products of elementary matrices. Question 3 Given 2 10 4 -1 1 0.…

A:

Q: 1 -1 0 1 Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible…

A: In the given question, the concept of the matrix is applied. Matrix A matrix is a rectangular array…

Q: [10-2] 1 1 6. Find the inverse of the matrix A = 2 2 3. if it exists. 14 2 5

A: