A · B = (7)(-3) + (-2)(4) = -21 - 8 = -29.

A · B = (7)(-2) + (-3)(5) = -14 - 15 = -29.

A · B = (ai + bj) · (ci + dj) = ac + bd.

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

A^2 = A * A = [[2*2 + 3*1, 2*3 + 3*4], [1*2 + 4*1, 1*3 + 4*4]] = [[10, 21], [21, 16]].

The inverse of A is given by (1/det(A)) * adj(A). Det(A) = (2*4) - (3*1) = 5. The adjoint is [[4, -3], [-1, 2]]. Thus, A^(-1) = (1/5) * [[4, -3], [-1, 2]].

Distance = speed × time = 60 km/h × 2.5 h = 150 km.

Area = πr², so r² = 50. Thus, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 14.14 cm.

Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.

Even numbers on a die are 2, 4, 6. Total outcomes = 6. Probability = Number of even outcomes / Total outcomes = 3/6 = 1/2.

The order of the product of two matrices is determined by the outer dimensions. Since both A and B are 2x2 matrices, their product AB will also be a 2x2 matrix.

The order of the product of two matrices is determined by the outer dimensions. Here, A (2x2) and B (2x3) can be multiplied, resulting in a matrix of order 2x3.

The maximum number of non-zero elements in the sum of two matrices occurs when all elements of both matrices are non-zero. Therefore, A + B can have a maximum of 9 non-zero elements.

The product of two matrices A and B, both of order 3x3, will also be a matrix of order 3x3.

The sum of two matrices of the same order results in a matrix of the same order. Therefore, A + B will be a 3x3 matrix.

The order of the resultant matrix when two matrices are multiplied is determined by the outer dimensions. Here, both A and B are 3x3, so the product AB is also 3x3.

The order of the sum of two matrices is the same as the order of the individual matrices. Therefore, A + B is a 3x3 matrix.

The sum of two matrices is defined only when they have the same order. Since both A and B are 3x3 matrices, A + B will also be a 3x3 matrix.

The product of two matrices A and B, both of order 3x3, will also be a matrix of order 3x3.

A 3x3 matrix has 3 rows and 3 columns, resulting in a total of 3 * 3 = 9 elements.

A 3x3 matrix can have a maximum of 3 linearly independent rows, but the answer options are incorrect. The correct answer is 3.

'c' represents the y-intercept of the line, which is the point where the line crosses the y-axis.

Setting x = 0 in the equation gives y = 8. Thus, the y-intercept is -8.

Setting y = 0 in the equation gives 5x = 60, thus x = 12.

Rearranging to slope-intercept form gives y = -7/2x + 7, so the slope is -7/2.

The y-intercept is the constant term in the equation, which is 6.

A matrix with more columns than rows is referred to as a rectangular matrix.

A matrix that is both upper and lower triangular must have non-zero elements only on the diagonal, making it a diagonal matrix.

In a diagonal matrix, all non-diagonal elements are zero.

A diagonal matrix has non-zero elements only on its main diagonal, while all other elements are zero.