Author: Study Clue

For any square matrices A,B of same order, det(I+AB) equals det(I+BA) when A Only if invertible B Only if symmetric

A matrix A satisfies Aᵀ = −A and is 4×4; det(A) can be A Always zero B Any real C

A square matrix A satisfies Aᵀ = A and has size A m ≠ n B 1 × n C

A 1×n matrix is commonly called A Row matrix B Column matrix C Square matrix D Null matrix Explanation A

A matrix of 3 rows and 2 columns has what order A 2 × 3 B 3 × 2 C

For φ = x²y + y²z + z²x, the directional derivative at (1,1,1) along u=(1,1,1)/√3 is A 10/√3 B 12/√3

For φ=x²y+yz², the gradient at (1,2,1) equals A A. (4,2,4) B B. (4,2,3) C C. (2,4,4) D D. (2,2,4) Explanation

For φ=xyz, the gradient at (1,2,3) equals A (6,2,3) B (3,6,2) C (2,3,6) D (6,3,2) Explanation ∇φ=(∂φ/∂x,∂φ/∂y,∂φ/∂z)=(yz,xz,xy). At (1,2,3) it

For φ(x,y,z)=x²+y²+z², the gradient at (1,1,1) is A (1,1,1) B (3,3,3) C (2,2,2) D (0,0,0) Explanation ∇φ=(2x,2y,2z). Substituting (1,1,1) gives

In vector calculus, the gradient of a scalar field gives what at a point? A Net flux B Circulation around