I only need the answers. I don't need any explanations kindly give me the answers from the options and numerical input.It will be helpful if you mark the answers on my question. I only have 20 minutes. If I get all the correct answers in time I will upvote. Consider the following system of linear equations:x + 4y + z = 3,Z = -1.Then which of the following is true?Select all possible answers.One of the variables is free.It is a homogeneous system of linear equations.It has exactly one solution.It has a non-trivial solution.{0000-11118Let Vbe a subset of R4. Recall that the span of any set of1vectors is a subspace. What is the dimension of span(V)?431{ei, e2, e3 }be an ordered basis for the vector space V. Suppose T : V → V is a linear1, 2and 3. Then thematrix (with the respect to the given basis B) that corresponds to the linear map T : V → V mustLet Bmap such that T(en) is the linear combination of the first n vectors of B for nbeSe'ect all possible answers.diagonalupper triangularlower triangularsingularnon-singularWhich of the following must be true?For any two n x nmatrices A and B, we must have AB =BAFor an invertible matrix M, we may find a large natural number n such that M" is NOT invertible.1()If M =1then M³ + M² = 2MThere are some non-invertible elementary matrices.()()1Suppose2andare the first two columns of a matrix A. If the RREF of the matrix A is311then the third column of the matrix A is0 0332There could be infinitely many possibilities for the third column of A. Let V be the set of all (5x5) real symmetric matrices. Recall that a matrix is called symmetric if it isequal to its transpose. It can be shown that V is a vector space over R with respect to usual matrixaddition and scalar multiplication. What is the dimension of the vector space V?101525Suppose M is a (11x11) matrix such that the dimension of its column space is 10 .Then the rank of MisSelect all possible answers.1110Let V be a 6 dimensional vector space over the set of reals. Then the dimension of a subspace of Vcould beSelect all possible answers.56.|4|3Recall that for any two given real vector spaces V and W, a function T : V → W is linear if T(ax+by) = aT(x)+ bT(y) for any vector x, y in V and for anyreal numbers a and b. Let T: R → R be a linear transformation such thatT= T1= T1Suppose10аT18Write down the value of a:Write down the value of b:Write down the value of c:Let M be a (7x7) matrix such that the dimension of its row space is 6. Which of the following is true?Select all possible answers.rank of Mequals to 6.Mis invertible.Mis not invertible.dim(columnspace(M))6.Let A be a (11x11) matrix such that the dimension of its column space is 11. ThenSelect all possible answers.dim (rowspace (A)) = 11Ais invertible.The determinant of Ais a non-zero number.A-' does not exist.Let A be a 3 x 3matrix with rank 3. Suppose there are two 3 × 3matrices Land U such that A = LU. Then which of the following is true?Select all possible answers.|rank(A) = rank(L)|rank(A) = rank(U).Both U and L are invertible.column space(A) = column space(L)L+Umust be invertible.Let A be the following matrix4 4 46.6Then for which column vector b, the equation Axbhas a unique solution?Select all possible answers.466аThe matrix U0 dmust have linearly dependent columns ife0 0f]f = 0|b =c=0e = 0a = 0

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I only need the answers. I don't need any explanations kindly give me the answers from the options and numerical input.It will be helpful if you mark the answers on my question. I only have 20 minutes. If I get all the correct answers in time I will upvote. Consider the following system of linear equations:x + 4y + z = 3,Z = -1.Then which of the following is true?Select all possible answers.One of the variables is free.It is a homogeneous system of linear equations.It has exactly one solution.It has a non-trivial solution.{0000-11118Let Vbe a subset of R4. Recall that the span of any set of1vectors is a subspace. What is the dimension of span(V)?431{ei, e2, e3 }be an ordered basis for the vector space V. Suppose T : V → V is a linear1, 2and 3. Then thematrix (with the respect to the given basis B) that corresponds to the linear map T : V → V mustLet Bmap such that T(en) is the linear combination of the first n vectors of B for nbeSe'ect all possible answers.diagonalupper triangularlower triangularsingularnon-singularWhich of the following must be true?For any two n x nmatrices A and B, we must have AB =BAFor an invertible matrix M, we may find a large natural number n such that M&#34; is NOT invertible.1()If M =1then M³ + M² = 2MThere are some non-invertible elementary matrices.()()1Suppose2andare the first two columns of a matrix A. If the RREF of the matrix A is311then the third column of the matrix A is0 0332There could be infinitely many possibilities for the third column of A. Let V be the set of all (5x5) real symmetric matrices. Recall that a matrix is called symmetric if it isequal to its transpose. It can be shown that V is a vector space over R with respect to usual matrixaddition and scalar multiplication. What is the dimension of the vector space V?101525Suppose M is a (11x11) matrix such that the dimension of its column space is 10 .Then the rank of MisSelect all possible answers.1110Let V be a 6 dimensional vector space over the set of reals. Then the dimension of a subspace of Vcould beSelect all possible answers.56.|4|3Recall that for any two given real vector spaces V and W, a function T : V → W is linear if T(ax+by) = aT(x)+ bT(y) for any vector x, y in V and for anyreal numbers a and b. Let T: R → R be a linear transformation such thatT= T1= T1Suppose10аT18Write down the value of a:Write down the value of b:Write down the value of c:Let M be a (7x7) matrix such that the dimension of its row space is 6. Which of the following is true?Select all possible answers.rank of Mequals to 6.Mis invertible.Mis not invertible.dim(columnspace(M))6.Let A be a (11x11) matrix such that the dimension of its column space is 11. ThenSelect all possible answers.dim (rowspace (A)) = 11Ais invertible.The determinant of Ais a non-zero number.A-' does not exist.Let A be a 3 x 3matrix with rank 3. Suppose there are two 3 × 3matrices Land U such that A = LU. Then which of the following is true?Select all possible answers.|rank(A) = rank(L)|rank(A) = rank(U).Both U and L are invertible.column space(A) = column space(L)L+Umust be invertible.Let A be the following matrix4 4 46.6Then for which column vector b, the equation Axbhas a unique solution?Select all possible answers.466аThe matrix U0 dmust have linearly dependent columns ife0 0f]f = 0|b =c=0e = 0a = 0

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Consider the following system of linear equations: x + 4y + z = 3, z = -1. Then which of the following is true? Select all possible answers. One of the variables is free. It is a homogeneous system of linear equations. |It has exactly one solution. It has a non-trivial solution.