Consider the following matrix:𝐴 = !𝑎 𝑏𝑐 𝑑'a, b, c and d are real numbersState whether each of the following statements is true or false. Explain.1 1DE XF D E- -=

Which of the following is true for matrices?Question 1Select one: (𝐴𝑇) = 𝐴 (𝐴𝐵)-1 = 𝐵-1𝐴-1 𝐴*𝐼 = 𝐴𝐴𝐵=𝐵𝐴

Which of the following is/ are TRUE?Determinant evaluated across any row or column is same.Determinant of a Identity matrix () is 1.If all the elements of a row (or column) are zeros, then the value of the determinant is zero.a.1 and 3 onlyb.3 onlyc.All of the aboved.None

Determine the validity of each statement by selecting True or False.  1. If a 3×3 matrix has eigenvalues 𝜆=−3,−1,2, then the singular values of the matrix are 𝜎1=3,𝜎2=2,𝜎3=1.  2. The SVD of any 𝑚×𝑛 matrix 𝐴 always exists and is unique.  3. It is possible for a 3×4 matrix to have the singular values 𝜎1=4, 𝜎2=0, and 𝜎3=−1.  4. If 𝐴 has linearly independent columns and 𝐴 has the SVD 𝐴=𝑈Σ𝑉𝑇, then the columns of 𝑉 form an orthonormal basis for Col𝐴.

[a b c] is a:Question 4Answera.Row matrix.b.Diagonal matrix.c.Column matrix.d.Zero matrix.

What are the truth values of these statements? a) ∃!xP(x)→∃xP(x) b) ∀x P(x) → ∃!xP(x) c) ∃!x¬P(x)→¬∀xP(x)