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 that B is an n x n matrix such that B²+B = I. Is B necessarily invertible? Justify your answer.

Q: A B D 5 -3 -5 3 Consider the matrix A - -4 -3 -31 1 0 4 4 ܝ ܀ What is the value of x so that A =…

A: To find out the value of x , we first find the adjoint of the given matrix. Then using the given…

Q: 2. (i) Find a matrix X such that (ii) Find a matrix Y such that 1 - 32] x = [3] X -2 21 53 Y = 0 2²…

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Q: -2 4 1 0 3 7 For the matrix B = what is the value of |B|? A. 8 B. 2 C. 4 D. -5 433

A: Given that, the matrix is B=1-24103373. Note that, the term B represents the determinant of B.

Q: b. Determine the inverse of the following matrix if it is invertible; 1 3 2 1 1 1 1 2 3 C = %3D

A: The given matrix is  C=132411123

Q: 1. Consider the following matrix: 17 3 1/3 -2 10 4 21 -12 -5 1/2 T e? 33 100 -17 16 1/4 -1 4 A = 1/2…

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Q: For the matrix A = 2 3 20 06 7 3 what is the value of |A|?

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Q: Q: Find the inverse (by any method you want) of the following matrix 31 1 4 3 1 3 4]

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Q: Show that the matrix below is not invertible. Use as few calculations as possible and justify your…

A: A square matrix A is said to be invertible if  . Otherwise A is not invertible.

Q: Please help with #5!

A: If the matrices, P, Q are invertible, then it can be written that PQ-1=Q-1P-1 .

Q: 3. Given matrix A below, answer if A is invertible or not. Provide your proof and calculate the…

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Q: 1 1 1 145 156 004 multiplied by D on the right or on the left. Find a 3x3 matrix B, not the identity…

A: Product of two matrix is possible when number of columns of first matrix is equal to number of rows…

Q: c. Using your answers from part b. above, calculate the matrix that will be derived from the…

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Q: Find 2 X 2 matrices A 0 and B # 0 such that AB = 0. Can you find a matrix A + 0 such that A2 = 0?

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Q: I keep trying and I can't get the answer to this question. I would really appreciate if someone…

A: The objective of the question is to find the (3, 1)-entry of X^-1 and the (2, 4)-entry of (X^T)^-1…

Q: -4 8. find the inyerse of the matrix ら -4 12 by Gaussian Jordan eliminaton methed

A: Given, a-48-412b6-c21100010001 Now take, R1→R14,R2→R24,R3→R33 Then, a4-12-13b42-c37140001400013

Q: 2 1 0 0 0 2 0 1 3. Let A and Ba 4 x 4 matrix with det(B) = 3. 0 3 1 -1 2 0 1 (a) (3 marks) Find…

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Q: Find the inverse of cach matrix if possible. If a matrix is not invertible, explain why. 3 0 1 2 2…

A: Matrix A is invertible if and only if  following conditions hold: 1. A must be n×n square matrix…

Q: 6.Compute the inverses of the following matrices: 85 16 2 3 12 -8 3 A = - B =

A: We have to find the inverse of the given matrices.

Q: 1 1 A = 01-1 0 0 4. Let (a) Use Gauss-Jordan method to find the inverse of A. (b) Write A-las a…

A: To find the elementary matrices and inverse of matrix using jordan method.

Q: For each of the following matrices, either find its inverse or say how you know it isn't invertible.…

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Q: 14. Which statements are true, and which are false? If the statement is false, provide a specific…

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Q: Calculate exp(A) where A is the 2 x 2 matrix given by [3 A = 7-2 5 5

A: Given a 2×2 matrix . We need to find its matrix exponential.The characteristic equation is,These are…

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: 8 9 11 12

A: matrix A is in dimensions 2*3 Matrix B is in dimensions 3*2 So multiplication of A and B= [AB] [AB]…

Q: 1 For the matrix A = 2 3 -2 0 7 4 6 3, what is the value of |A|?

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Q: 4. Construct the truth tables for the following statements to determine whether each of the…

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Q: Which of the following statements are true? I. If A and B are invertible matrices with A = (B?)-1,…

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Q: Q3. Diagonalise the matrix [A]. 4 33 [A] = 3 6 1 3 1 6

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Q: -1 1 Verify that the matrix A = 3 is diagonalizable; 4 -2 5

A: We will use condition for matrix to be diagonalizable

Q: 1. The matrix J is given by J= a) Show that J² d -b -C $] a [a b]. c d where a+d=-1 and ad-bc=1.

A:

Q: If A and B are n x n matrices, then (AB)T = A. AT BT B. AT + BT C. (BA)T D. BT AT

A: given  A and B are n×n matrix

Q: -2 I 5 2 Find the inverse of the above matrix in three different ways

A: Let's find.