If (zero matrix) has only the trivial solution then has a unique solution for all choices of in .

Suppose A is a 3 × 3 matrix and y is a vector in R3 such that the equationAx = y does not have a solution. Does there exist a vector z in R3 suchthat the equation Ax = z has a unique solution? Why?

Let A be 3×3 matrix with rank 2.Then AX=0 has A. Only trivial solution X=0 B. One independent solution C. Two independent solution D. Three independent solution

If a matrix has determinant zero then it is singular matrix.Select one:TrueFalse

Which matrix has most of the elements (not all) as Zero?Select one:a.Identity Matrixb.Unit Matrixc.Sparse Matrixd.Zero MatrixClear my choice

Pick the odd one out.Question 4Select one:𝜆 is a solution of the characteristic equation 𝑑𝑒𝑡 (𝜆𝐼 - 𝐴) = 0.𝜆 is an eigen value of A.There is a nonzero vector x such that 𝐴𝑥 = 𝜆𝑥.The system of equations (𝜆𝐼 - 𝐴)𝑥 = 0 has trivial solutions.