Let A be an n x n matrix. Are the following statements true or false? ? 1. If 5 = 0 then det(A) = 0. ? 2. For any n x n matrices A, B, det(AB) = det(A) det(B). ? 3. If the null space of A is {0} then det(A) = 0. 4. If A is a 3 × 3 matrix with zero determinant, then one column of A must be a multiple of the other one. ? 5. Let A be any square matrix. det(ATA) ≥ 0 ? 6. The determinant of B is defined for all matrices B ? 7. If A is in REF form then det(A) = 0 or 1. 8. If the rref of A is I then det(A) is 1. 9. If det A = 3 then det(24) = 6. 10. If A is a 2 x 2 matrix with zero determinant, then one column of A must be a multiple of the other one.

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Q: -1 004 -1 1 04 1 -2 0 3 2 0 -3 -2

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Q: Every matrix has its determinant. O True False

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Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

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Q: Identify all of the true statements below about elementary matrices. Any elementary matrix that adds…

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Q: 2. Find for the determinant of the given 5x5 matrix. Identify the resulting 4x4 matrix using matrix…

A: Explanation of the solution is given below...

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Q: Which of the following is FALSE? A. Det (AB) = Det (A) + Det (B) B. Det (AB) = Det (A) Det (B) T C.…

A: The False statement is  Det(AB)= Det(A) + Det(B)

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Q: If a 4 x 4 matrix A with rows ₁, ₂, 3, and 4 has determinant det A=-5, 601 +7 4 then det V2 V3 401…

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Q: If B = then the determinant of B~1 is_ - (use property) a. 2 d. b. 10 с. 0.5

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Q: Find the inverse of the matrices 7. A = -5 2 5 15 3. - 3

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Q: If A is a 3 x 3 matrix with two identical columns. Which one of the following statements is true? A.…

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Q: 5. Consider the following four matrices: ab c ba 2a 2b 2c a-3c b+Sa A= d e f #ME B-f d de f D d-3f…

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