Suppose A and B are 3x3 matrices with det A = 2 and det B = -3. Find det(2BTA-B).

Q: Show that if A and B are positive definite matrices, then A® B is positive definite.

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Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: If A and B are n × n diagonal matrices, show that AB = BA.

A:

Q: Find inverse matrix using Gauss - Jordan Method if available 1 -2 4 A = 2 8 -1 -3 -4)

A: To find the inverse matrix, augment it with the identity matrix and perform row operations trying to…

Q: For any 3x3 matrices A & B: Verify that (AB)" = B" A".

A:

Q: Suppose A. B and X are 'nxn matrices such that A and B are invertible, and Which one of the…

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Q: Show that AB and BA are not equal for the given matrices.

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Q: Create two 2 x 2 matrices A and B, to show that (A+ B) - A+B is not always true. Clearly write A, B,…

A:

Q: Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

A: See the attachment

Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given: -243-1

Q: If A and B are matrices 3 x 3 order with 12A| = -1 and |2B³| = 16, then calculate |A-1B"|.

A: Here, A and B both are of the order 3×3. So, A-1 and BT are of the order 3×3. Now, from the…

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B) Upload an image or PDF of…

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Q: If A=2B where A and B are square matrices of order 3x3, and det(B)%3D5, what is det(A)? Select one:…

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Q: 3. Give an example of two 2 × 2 matrices A and B for which (AB)² # A²B².

A: To prove above equation with an example

Q: For any two 3 x 3 matrices A and B, we have (А + B)(А — В) — А? — АВ + ВА - В?

A: Given statement: For any two 3×3 matrices A and B, we have

Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: Suppose that both A, B ore 2x2 matrices such that det (A) = 2, det (B)=6. Then det (AB) = %3D det…

A: As per our guidelines only 3 sub-parts can be solved: Solving 1st three sub parts in the steps…

Q: 2 if A=| -3 -2 4 and B= 1 ,find the Matrix X such that 3A+4X=5B 1 3

A:

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A" A-1)?

A: Given that A,B and C are 3*3 matrices. To find det(A^TA^-1)

Q: Given two matrices A and B, how can you determine the order of AB, assuming that the product is…

A: Let order of A is mxnAnd let order of B is nxp (because product of AB is defined)

Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A:

Q: Find three 2 × 2 matrices, A, B, and C such that AB = AC with B = C and A = O.

A: Consider the matrices A=0000,  B=1234  and  C=1234. Clearly, B = C and A = O.

Q: If A and B are nXn matrices, then (A-B) =A-2AB+B Select one:

A: A-B2=A-BA-B=A2-AB-BA+B2

Q: Show by direct calculation for 2x2 matrices A, B, C that A(BC)

A: To prove that  for 2×2 matrices A, B,  that A(BC)=(AB)C.

Q: The product of two non-zero matrices is always non-zero. Select one: O True O False

A: the product of two non zero matrices is always non zero

Q: if A and B are 3x3 matrices such that det(A) = -5 and det(B) = 4, find the values of the following…

A: If A and B are 3x3 matrices such that det(A) = -5 and det(B) = 4, find the values of the following…

Q: If A and B are 3 × 3 matrices and detA=2 and det B = 4, find det (5A* BTΑ-)

A: See the details solution in below

Q: Are the two matrices similar? If so, find a matrix P such that B-P-AP. (If not possible, enter…

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Q: Find inverse matrix using Gauss - Jordan Method if available [1 3 4] A = |1 -5 0 [3 -2 4]

A: Lets name the given matrix say A To find inverse of A using gauss jordan method  we first take the…

Q: 3 - 3 1 /- 1

A:

Q: If A=2B where A and B are square matrices of order 3x3, and det(B)%3D5, what is det(A)? Select one:…

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Q: Find the matrix B such that 2AT+3B=0.

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Q: Let A and B square matrices where detA=4 and detB=12. What is det(A-1B)?

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Q: If A and B are nXn matrices, then (AB)²=A²B? A True

A:

Q: Find the inverse of the matrix if it exists. 4 2 3 3 3 2 1 0 1

A: Inverse of a matrix exists if the determinant of the matrix is non-zero.Here the given matrix is-

Q: Consider the two matrices: 2 4 1 B= -5 A= -3 Compute A+ 3B. The result is equal to:

A:

Q: Create two 2 x 2 matrices A and B, to show that (A+ B)- A +B is not always true. Clearly write A, B,…

A: Give an example of 2 × 2 matrix, in which A + B-1 = A-1 + B-1 is wrong.

Q: . We can add (or subtract) two matrices only if they have thesame .

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Q: If a and b are the matrices of order 3 and (A)=5,(b)=3 then find the vailue of 3ab?

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Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: Find the matrix product AB, if it is defined. 3 -2 1 B: 3 0 4 - 3 -2 3

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Q: Find inverse matrix using Gauss - Jordan Method if available 1 -2 4 A = 8 [-1 -3

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

Q: Show by counterexample that (AB)−1 ≠ A−1B−1. That is, find two matrices A and B for which (AB) -1 ≠…

A: Let