Question

Calculate the determinant of the matrix: | 4 1 6 | | 3 0 2 | | 5 8 7 |​

Answer 1

Answer:69

Explanation:

Matrix determinant:

Matrix:

matrix([4,1,6],[3,0,2],[5,8,7])

Result:

69

Answer 2

↪ To calculate the determinant of the 3x3 matrix:

| 4 1 6 |

| 3 0 2 |

| 5 8 7 |

You can use the following formula for a 3x3 matrix:

det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

Where the matrix is:

| a b c |

| d e f |

| g h i |

In your case:

a = 4, b = 1, c = 6

d = 3, e = 0, f = 2

g = 5, h = 8, i = 7

Now, plug these values into the formula:

det(A) = 4(0*7 - 2*8) - 1(3*7 - 2*5) + 6(3*8 - 0*5)

Calculate the individual products and differences:

det(A) = 4(-16) - 1(21 - 10) + 6(24 - 0)

Now, perform the calculations:

det(A) = -64 - 1(11) + 6(24)

det(A) = -64 - 11 + 144

Finally, add the numbers together to find the determinant:

det(A) = -64 - 11 + 144 = 69

So, the determinant of the matrix is 69.

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