Let A and B be n xn matrices. Determine whether the statement below is true or false. Justify the answer. det(A + B) = det A + det B Choose the correct answer below. O A. The statement is true. Determinants are linear transformations. 1 0 - 1 O B. The statement is false. If A = and B = then det(A + B) = 0 and det A + det B = 2. 0 1 - 1 2 0 3 0 O c. The statement is true. If A = 1 0 and B = then det(A + B) = 0 and det A + det B = 0. 5 0 O D. The statement is false. det(A + B) = (det A)(det B)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let A and B be n×n matrices. Determine whether the statement below is true or false. Justify the answer.
det(A+​B)=det A+det B
Let A and B be n xn matrices. Determine whether the statement below is true or false. Justify the answer.
det(A + B) = det A + det B
Choose the correct answer below.
O A. The statement is true. Determinants are linear transformations.
1 0
- 1
O B. The statement is false. If A =
and B =
then det(A + B) = 0 and det A + det B = 2.
0 1
- 1
2 0
3 0
O c. The statement is true. If A =
1 0
and B =
then det(A + B) = 0 and det A + det B = 0.
5 0
O D. The statement is false. det(A + B) = (det A)(det B)
Transcribed Image Text:Let A and B be n xn matrices. Determine whether the statement below is true or false. Justify the answer. det(A + B) = det A + det B Choose the correct answer below. O A. The statement is true. Determinants are linear transformations. 1 0 - 1 O B. The statement is false. If A = and B = then det(A + B) = 0 and det A + det B = 2. 0 1 - 1 2 0 3 0 O c. The statement is true. If A = 1 0 and B = then det(A + B) = 0 and det A + det B = 0. 5 0 O D. The statement is false. det(A + B) = (det A)(det B)
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