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For which k value, the matrix is not invertible? 3k 12Oa) 1b) 2None of thesed) 3-4...

Question

For which k value, the matrix is not invertible? 3k 12Oa) 1b) 2None of thesed) 3-4

For which k value, the matrix is not invertible? 3k 12 Oa) 1 b) 2 None of these d) 3 -4



Answers

find the values of $k$ for which the matrix $A$ is invertible. $$A=\left[\begin{array}{cc} k-3 & -2 \\ -2 & k-2 \end{array}\right]$$

We want to find the values of K. For which matrix A is inevitable given the three by three matrix A with Rose 124316 K 32 So this is also emerged in the upper right of the document. So in order to figure out whether or not this matrix is convertible for certain values. Okay, we're going to use the determinant in the relationship between the determinant. Invert ability to solve who to start off with. The determinant of a three by three matrix with rows A B C D E f G H I is given as follows on the left and that matrix or Matrix A is in veritable if and only if the determinant does not equal zero. So let's apply the formula on the left and then solve for K. Or rather where the determinant is equal to zero for certain 1000 K. To solve this problem. So the determine of A is simply one time two minutes 18 minus two times 616 K plus 4 29 minus K, which reduces down to eight plus A K. If we solve for zero, we have the equals a. K, equals zero, or K equals negative one. In order for the determined to be zero. So that means that this matrix is in veritable whenever K does not equal negative one.

All right. We find, we want to find the values of K. For which the matrix A. Is convertible. Where A has rose K two and two. K. A is simply a two by two matrix given here in the upper right of the document. So in order to answer this question, we need to be able to take the determinant of K. Or rather disturbing enough Matrix A. And identify from that determinant where A is not convertible to do so we make a note of the fact that the determinant of a matrix A. B C. D. Is A. D minus C. B. And that matrix matrix A is inevitable if and only if the determinant does not equal zero. So we need to solve for the determinant and identify for what values of cable determinant does not equal zero. So to start off, the determinant of A is simply keychains K minus four or k squared minus four. We solve that for zero. Sochi experiments for equal zero, which reduces the case critical for or K equals plus or minus two. When the determinant zero, so monkey equals minus two, the determinant zero Ak is not inevitable, so that means that A is convertible whenever K does not equal plus or minus two.

We want to find the values. Okay, for which matrix A is convertible, matrix A is a three by three. Matrix throws 1 to 0 K. One K. M 0 to 1. As shown in the upper right. To solve this problem, we're gonna use the relationship between the determinant and matrix convertibility. Remember that to find the determined about three by three matrix with rows A B c, D e, f g h I. We use the formula here on the left. Then we can use the fact that A is inevitable if and only if it's determined does not equal zero. So we want to find where from the determinant formula. Certain values of K. Make are determined zero and go from there. So first applying the formula, the left, the determinant of A is one times one minus two K minus two. James, t minus 00 or two minus four K. So solving for zero, we have two minus four K equals zero or 14 equals two or k equals one half. That means that are determinant is zero and that is not inevitable when K equals one half. So we must have that Matrix A is convertible whenever K does not equal one half.

Hello there. So for this exercise, we need to find the values off K such that a is not convertible or, in other words, a become singular. Okay, So what are the conditions for the matrix to become singular? Well, we need to check that The determinant. Actually, we need to ensure to the determinant is equal to zero. Okay, so the determine off this matrix is equals to four times K plus six, and this should be equals to zero on. We're going to solve this equation for K. So K is equal to minus six, divided four. But this is just gate. It's equals two minus three halfs. So if K is equal to three house, then the matrix is singular, and there is no inverse for these matrix.


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