The determinant is 0 because the first column is repeated.

The determinant is 0 because the rows are linearly dependent.

The determinant evaluates to -12.

The determinant is 0 because the rows are linearly dependent.

The determinant is 0 because the rows are linearly dependent.

The determinant is 0 because the rows are linearly dependent.

The determinant is calculated as \( 2(0*1 - 2*4) - 1(1*1 - 2*3) + 3(1*4 - 0*3) = -10 \).

The determinant is calculated as 2(0*1 - 2*2) - 1(1*1 - 2*3) + 3(1*2 - 0*3) = 2(0 - 4) - 1(1 - 6) + 3(2) = -8 + 5 + 6 = 3.

The rows are linearly dependent, hence the determinant is 0.

The determinant is 0 because the rows are linearly dependent.

The determinant of the identity matrix is 1.

The determinant of a matrix with linearly dependent rows is 0. Here, the rows are linearly dependent.

sin^(-1)(1) = π/2 and cos^(-1)(0) = π/2. Therefore, π/2 + π/2 = π.

tan^(-1)(1) = π/4, so the expression becomes π/4 + π/4 + 0 = π/2.

tan^(-1)(1) = π/4, thus tan^(-1)(1) + tan^(-1)(1) = π/4 + π/4 = π/2.

tan^(-1)(1) = π/4 and tan^(-1)(√3) = π/3. Therefore, π/4 + π/3 = 7π/12.

The determinant of the identity matrix is 1.

The determinant is calculated as \( 1(1*1 - 0*3) - 2(0*1 - 0*2) + 1(0*3 - 1*2) = 1 - 0 - 2 = -1 \).

The determinant is calculated as \( 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = -24 + 40 - 15 = 1 \).

The determinant is \( 2*3 - 1*1 = 6 \).

sin^(-1)(0) = 0 and cos^(-1)(0) = π/2, thus the sum is 0 + π/2 = π/2.

sin^(-1)(1) = π/2 and cos^(-1)(0) = π/2. Therefore, π/2 + π/2 = π.

a_10 = 3(10) + 2 = 30 + 2 = 32.

a_10 = 3(10^2) + 2(10) = 300 + 20 = 320.

The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = 3π/4.

The coefficient of x^0 is C(4, 0) * (2x)^0 * 3^4 = 1 * 81 = 81.

The coefficient of x^1 is C(5,1) * 2^4 = 5 * 16 = 80.

The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^4 = 15 * 9 * 256 = 34560.

The coefficient of x^3 is C(6,3)(2)^3(-3)^3 = 20 * 8 * (-27) = -4320.

The coefficient of x^3 is C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.