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Asked Sep 17, 2019

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(8) (Section 3.8, # 15) Suppose a 2x2 matrix A satisfies the following equation:
0 2
A
1
1
4
Without calculating the entries of A, find det(A)
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(8) (Section 3.8, # 15) Suppose a 2x2 matrix A satisfies the following equation: 0 2 A 1 1 4 Without calculating the entries of A, find det(A)

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Expert Answer

Step 1

Given equation is:

Determinant of a matrix is given by:

According to the properties of determinant...

0 2
A
1
2
2
1
4
b
а
М
c d
det (M
ad bc
det (A) x det (B) = det (AB
0 2
det (A) x det
1 2
1 2
det
1
det (A)x ((0)(2)(2)(1))
det (A)x (0-2)(-4-2)
det (A)x (-2) (-6)
det (A)x (-2) (-6)
(-2)
((-1)(4)-(2) (1))
(-2)
det (A)3
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0 2 A 1 2 2 1 4 b а М c d det (M ad bc det (A) x det (B) = det (AB 0 2 det (A) x det 1 2 1 2 det 1 det (A)x ((0)(2)(2)(1)) det (A)x (0-2)(-4-2) det (A)x (-2) (-6) det (A)x (-2) (-6) (-2) ((-1)(4)-(2) (1)) (-2) det (A)3

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