17. Let [12 A¹ = 0 3 1 412 If possible, find a matrix C such that --- ACA = 2 1 3] 2 2 214 -1

Q: Let A be an 7 × 7 matrix in which every entry is 1 and I7 be the 7 × 7 identity matrix. Prove that…

A: Matrix 'A' is  defined such a way that , all the entries are 1 of order 7×7. Some results: If sum…

Q: 2. Compute (3C – 4D)², where C and D are arbitrary n x n matrices. Hint: Remember that matrix…

A: To compute, 3C-4D2

Q: 17- Let A be 5 x 5 matrix and det(4) = 2. What is the value of der(24)? a) 128 b) 32 16 64 LEave…

A:

Q: 04) X = [ Y = ; Hand Z = [ 3 Q.4) X Prove the Distributive laws of multiplication over Subtraction…

A: The given matrices are X=23-10,Y=0131  and  Z=22-10. The distributive law of multiplication over…

Q: .

A: We will use the inverse of 2x2 matrix formula

Q: 6. Given real m×n matrix A, real nxp matrix B and real number c, prove: c(AB)= (cA)B

A: The product of matrix A and matrix B is possible because the number of columns in matrix A is equal…

Q: .

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Q: 1 A = )Find the rank of a matrix 7 17 1 - 2 | 3.

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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.

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Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: 9. Show that the matrices (6) 65), (8), and (1) generate M2×2(F).

A: We have to show that the matrix  and  generate

Q: 7. Let A be an 7 × 7 matrix in which every entry is 1 and I, be the 7 × 7 identity matrix. Prove…

A:

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 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

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Q: 1. If 1+ A is nonsingular, show that (I+ A)"' and I– A commute and (I + A) +(I+ A')"=1, where I is…

A: Given I+A is nonsingular and we have to show that I+A-1 and I-A commute and  I+A-1+I+A-1-1=I

Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

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Q: [o 5 Write down the quadratic form corrsponding to the matrix 5 1 -1] -1 6 2 6

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Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

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Q: Given that P= (ad), 428 Engineering Mathematics where a +d=-1 and ad-be = 1, show that and hence…

A: Given Problem:- p=abcd Given a+d=-1 and ad-bc=1 Show that  p2=d-b-ca Hence deduce that  p2+p+1=0