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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]arrow_forwardConsider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of B and the column vectors of AB are in the column space of A.arrow_forward11. Find two nonzero matrices and such that.arrow_forward
- Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.arrow_forwardDetermine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.arrow_forwardLet A be a 2 X 3 matrix, B be a 3 X 2 matrix and v be a 3 X 1 vector. Indicate the dimensions of the resulting matrices or indicate if such operation is undefined by writing u x u a. AB is b. (Av) is c. AB-¹ is d. BAT ^+^ is e. v+v¹ is X X X X Xarrow_forward
- and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. Let y = (Type an integer or simplified fraction for each matrix element. List the terms in the same order as they appear in the original list.) Enter your answer in each of the answer boxesarrow_forwardThe set of non-zero vectors {b,, b,, bz, b4} are vectors in R* with the property that 4b, + 2b, = 6b, . Let matrix B = | b, b2 b; b4. (a) What does the matrix b, b, b, reduce to in RREF form? (b) Find a specific solution to the matrix equation Bx = 0. That is, find an x vector that solves that equation. (c) What is the maximum number of pivots matrix B can have? Please explain briefly referencing anything from above. (d) Can the set of vectors {b1, b2, b3, b4} span R’? Explain why or why not? (e) Can the set of vectors {b,, b2, b3, b4} span R*? Explain why or why not? (f) Matrix M is 7 x 4. If possible, show that the columns of the matrix MB are linearly dependent. If it is not possible to show this, explain why.arrow_forwardIf the column space of a 3x3 matrix consists of all vectors b=[b¡ b2 b3] such that b1+ b2= 3b3 then one of the following set of the vectors forms abasis for the left null space of that matrix: O [ 11 - 3] O[113] and [11 -3] O[33-1] O[33 1] and [3 3 - 1]arrow_forward
- Find a basis for the row space ofarrow_forward4. Describe all matrices row equivalent to the matrix: 3 -2 -[:] [] 0 2 3 (a) List five vectors in Span{V₁, V₂}. For each vector, give the corresponding weights. (b) Give a geometric description of Span{V1, V2}. 5. Consider the vectors: V₁ = and v₂ = 1arrow_forwardCalculate the 2X2 matrix A for which £, (2) ₁ Eo = span { -(3) 5 that is. all e- vectors associated to the e-value à can be written as a real number number times v. } and E₂= span { The first row of A has entries The second row of A has entries } where E = span {v}, λ and andarrow_forward
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