Evaluate the determinants of each of the following matrices in two ways, using the indicated rows and columns. Observe that you get the same answers both ways. 1 2 -3 0 3 (a) 4 1 3 1st row (1) x - (2) x + (-3) x = 1st column (1) x - (0) x + (4) x = 5 6 (b) 2 -6 1 2 7 6 3rd row (2) x - (7) x + (6) x 2nd column -(5) x + (-6) x (7) x
Evaluate the determinants of each of the following matrices in two ways, using the indicated rows and columns. Observe that you get the same answers both ways. 1 2 -3 0 3 (a) 4 1 3 1st row (1) x - (2) x + (-3) x = 1st column (1) x - (0) x + (4) x = 5 6 (b) 2 -6 1 2 7 6 3rd row (2) x - (7) x + (6) x 2nd column -(5) x + (-6) x (7) x
Evaluate the determinants of each of the following matrices in two ways, using the indicated rows and columns. Observe that you get the same answers both ways. 1 2 -3 0 3 (a) 4 1 3 1st row (1) x - (2) x + (-3) x = 1st column (1) x - (0) x + (4) x = 5 6 (b) 2 -6 1 2 7 6 3rd row (2) x - (7) x + (6) x 2nd column -(5) x + (-6) x (7) x
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Transcribed Image Text:Evaluate the determinants of each of the following matrices in two ways, using the indicated rows and columns. Observe that you get the same answers both ways.
1 2 -3
(a)
0 3
4 1
3
1st row
(1) x
(2) x
|+ (-3) ×
1st column
(1) x
(0) x
+ (4) x
5 6
(Б)
2 -6 1
7 6
3rd row
(2) x
(7) x
+ (6) x
2nd column
-(5) x
+ (-6) x
- (7) ×
O N N
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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