LINEAR ALGEBRA LATEST COMPLETE EXAM QUESTIONS WITH CORRECT DETAILED ANSWERS UPDATED 2025/2026 ||A+ GRADED

LINEAR ALGEBRA LATEST COMPLETE EXAM QUESTIONS WITH CORRECT DETAILED ANSWERS UPDATED 2025/2026 ||A+ GRADED 1) domajn - ANSWER set R^n (column) 2) codomain - ANSWER set R^m (row) 3) range - ANSWER set of all linear combinations of the columns of A because each image T(x) is of the form A(x) 4) m - ANSWER row 5) n - ANSWER column 6) Linearly Dependent - ANSWER nontrivial solution 7) Linearly Dependent - ANSWER set contains zero vector 8) Linearly Dependent - ANSWER contains linear combinations 9) Linearly Dependent - ANSWER more vectors than entries 10) Linearly Dependent - ANSWER contains free variable 11) Linearly Independent - ANSWER only trivial solution (zero vector) 12) Linearly Independent - ANSWER 2 non parallel vectors 13) consistent system - ANSWER at least one solution 14) unique solution - ANSWER only one solution 15) row x column - ANSWER m x n 16) vector equation - ANSWER y= c1v1 + c2v2 + ... + cnvn. (c are constants) 17) Matrix equation - ANSWER Ax=b 18) coefficient (NOT augmented) - ANSWER Ax=b is consistent is the ___________ matrix of [A b] ha a pivot in every row 19) homogenous equation - ANSWER Ax=0 20) zero - ANSWER trivial solution 21) parametric vector equation - ANSWER x=p+tv 22) standard basis vectors - ANSWER e1, e2, e3, e4... 23) thm 10 - ANSWER let T: R^n --R^m be a linear transformation. Then there exists a unique matrix A such that T(x)=A(x) for all x in R^n. 24) transpose - ANSWER mxn -- nxm 25) NOT invertible - ANSWER if ad=bc 26) invertible - ANSWER if ad does not equal bc 27) A^(-1) - ANSWER 1/(ad-bc) [d -b] 28) [-c a] 29) elementary matrices - ANSWER (Anxm | In) --- (In | A^(-1))